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Full text of "Armenian Theory of Special Relativity"

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2-82 



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2007p. 



1 - Upiujuiip Injhpp <iupiupapuilpuQ CiupdiSiuQ "blpxipiuqpnuip (4-6) 

1.1 - Upiujuup Injhpp cfmdmQiulpiiitiiupiu&uijpQ QUunpnJunipjiuCi ^uiqMjiuuipiuiSQhpp (7-9) 

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1.3 - <wpwpapmlpxiQnipjmQ <piSQwiyinijpp Oqinuiqnp&nuSp 

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U ^lulpnqpp I^Qhpgpuq <uuiiul}iupqhpp UuihiSiuQnuSp (32-39) 

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U Piugiupdiuq UpuiqmpjiuQ QUiuipnJunipjiuQ 4,iuq'iuuiupniiSQhpp (46-52) 

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4,nmiiQap - (82) 



© O-blpntuSphp - 2012p., n-nphpui \>iuqiupjiuQ U 4iujl[ X>iuqiupjiuQ, UpfuJuiQ 

<hnJiQiuqiujpQ ppuupuQpQapp. 1-867641991 , 21 ahlpnhiSphpp 2012p., UlTb, (Copyright Office) 

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3-82 



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4 -82 



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Iv'l*lvl 1-0- 

Ujuuipurnl hplpu quiduijuiquiG K' U K hGhpgpuq huiduiquipqhpp uinuiGgpuipi|hpp dpgh mnjiq h huilpjjquipd 
duuupnpinipjuiG huii|uiuuipnLdGhpp, uidhGuipGnhuiGnLp qtuqpmd IpuGhGuiG htunLjuq Ipjjpjijuj&nipjniQp. 

flinjiq 6Uuii}inJunipjniQQtip <uiquiquipd 6UuiipnJunipjmQQtip 

t' = t'(t,x,v) \ t = t(t',x',v') 1-b 

x — x (t,x, v) x = x(t ,x ,v ) 

Cun.q&niil 1-2 - bpb iSGGp oqmi[hGp (1 - l~)-/i hppnpn JifaifGiunpmjp/ig, hiuiSwdwjG npji hwpwphpiulpuGmpjiuG hwuiml] 
mbumpjwG Gbp pnpip liGbpgJimi hwUwbwpqbpnid dwiSuiGwtyp L mwpwdnipjniGp hwiSwubn bG, wupu hGuipwGnp t 
mupugmgbi, np (1 - \j)-nU inpdiud hwpiupbpwlpuG ^wpdtSwG wiSbGiupGnhwGmp mnfin b huibuupupd dbimpnpjmpjwG 
hwdwuwpmilGhpp, puin dmGwGwljfi b mwpwdnipjwG, niGbG q&wjIiG l]iupjilwdnipjmG [2], [4], [6].' 

TjUihipuiG dpui^uuh qnjhpp duiduiGuilpjjLnuipui&uijpG dhuiipnhinLpjuiG huliluiuuipnidGhpp uipuiui&duiG uiGgGtqp 
GhplpjjjuigGhGp pQhpgpuq hiuduiquipqhpp npuilpiilpuQ uibuiuqQhpp: bpl}^uaipuiQp duiduaQuiljuiinuapui&nipjiuQ dhg qnjmpjmQ 
niQhQ pQhpgpun huidiul}uipqbpp hpl}m Junidp' uigiJil} pQhpgpun hiuduil}uipqtip U duijuipq pQhpgpun huiduiqiupqhp: Ujipq 
quid fiiupJiJil} pQhpgpuq hiuduil}uipqhpp diuduiQuil}iuinuipui(JiuquiQ hiuppmpjuiQ dhg upmnhpiq' hpphp fipuip hhtn ^hQ 
huidpQljQp: <binUuipuip qpiuQp npiul}uiiqhu iniupphp pGhpgpuiL huiduiqiupqhp hQ: '-Lhpnhp2Jiut uigiJilj U duijuipq pQhpgpun 
huiduiquipqhpp nqg uinuiQfiQuihuiinqnipjniQQhpp pjjq^iuqnijQu p huijin qquiQ hnui^uiip 5>pqpquiliuiQ uiuipui&mpjuiQ Ipud 
piuniu^uiip duiduiQiulpiiiniupui&nipjuiQ dhg: Uhui hplj^uiip dunSuiQuiljuiinuipui&nipjuiQ dhg pGhpgpuiL huiduiqiupqhpp 
uinuiQgpQhpp niqqil 111 ^ 11 ^ 111 ^ P n L n P hQuipuiilnp uiuipphpuil}Qhpp h npuil}uiquiQ muipphpnipjniQQhpp: 

1 . UupuqimShin wpifib b wGgjwnuiSbm dwpJipli pGbpgpuj[ hwiSiulpupqbpp mpUiuq&ilwcr bG uumpb 

[ 



ILuiuiqunihui 



U21W 

-> x 



f t— - -t 

\ X— -X 



auijuQiij 




UQgjuiiuiiltiui 

q.&uiq]iji 1 t 

(Q-friuqlip 1)-p dhg, uig Ijnqdp uiQgjuipjjdhin duijuipq pQhpgpun huiduiqiupqp iquiuihpiil 180°-nd t , uijQ IjhuidpQqQp duiju 
qnqdp uiiquiqiudhui uigiJil} pQhpgpuq huiduil}iupqp hhui: 



5-82 



^mjlpjiqiuG <uipuiphpuil)uiQnipjujQ <uiuiiulj ShumpjiuG 

2. UupuquiiShm diufuijib L wGgjwiwiSbm iug]]ib pGbpgpaii hwGiubwpqbpp mpUwqdi/ui& bG uumph 

t 



UuiLuqiuiibin 



OmJu[Jil} 



{ — "' 

(.X— +x 



x -s * u r > x 



ft — +t 

\ X — i- -X 



uaiH 



Urigjiuiunlbin 

Q-&tuq]iji 2 t 



(Q-cJiuqpp 2)-Ji ui$> qnrpjfi uiGgjuipuiihui uagjjili JiGhpgJiuiL huiiSiuquipqp upnuihpiq' 180°-ni[, uijQ ghuiiipGqGp duiju qnrpJJi 
luupuqiuiitiin diupaiJil} pQbpgpunhuidiul}LupqJi hhui: 



lljuiqjiuni[, diuiiuiGiuquiuiuipiu&nipjuiG iSh$>, lihQp qiuGhGuiGp npuiquiiqhu ppuippg uiuipphp hhuiUj ui^ hplpii pQhpgpun 
huiiSuiquipqhp < uiupuquiiihui uijiliq U uiiquiquiiShin duijui|iq, npnGp nipq'uiq&il ul <J bfl uuinpU. 

UglJil} pQhpgpun hiuiiiul}uipq Qiujiqplj pGhpgpuiL huiiiuiljuipq 

t t 

Uquiquiilhui Uuiuiquiiitiin 




112 (Jill , SuifuiJil] 

-» x La x *- 



Q-friuqJip 3 



o 

1 1 — +t 

\ x— - -x 



(Q-fruiqpp 3)-[i ui$> linqiSJi fiuipaiJil} pGhpgpLULhuniiulpjipqp huiGnJiuuiGnuS t uijiJil} pGhpgpuiL huiduil}uipqji inuipiu&iulpjiG 
huijhpjijpG uiQqpuiqiupfiniiJp: 

"blpmnp niGhGuipiq' dpiu^uiip uiuipui&nipjiuQ lib? npiulpjiiqhu Jipuipjig inuipphp hplpu fiQhpgJiun huiiSuilpjjpqDpp 
qnjmpjuiG ifiuiuinp, lihQp uiQhpiudh2Uiuipuip iqhuip t uuiMuiGaQp qpuilpjiG U puigiuuuilpuG dUuiqinJunipjniQQhpp: 

Uuihdiulinul 1-1 

♦ IpwljiuG dbwipn[iimpjmGGhp 



UjG dhwipnpjmpjmGGbpp, npnGp wpiph pGbpgpwi hwdwbiupqp pnqGmii bG wpipq pGbpgpiui hwrfwhiupq Ipurf dwpiiplj 
pGbpgpwi hwdwbwpqp pnqGmii bG dwpjjjil] pGbpgpwi hwUwqwpq, li'bGp bwGUwGbGp qpwbwG dhwipnpjmpjmGGbp: 



1-2 



♦ fiwgwuwbwG dbwipnpimpjmGGbp 



lljG dbwipnpimpjmGGbpp, npnGp wp/Jib pGbpgpwi hwdwbwpqp qwpdGniU bG dwpjjjiq pGbpgpwi hwdwqwpq bwif dwpiipu 

1-t 
pGbpgpwi hwUwqwpqp qwpdGmii bG uipiph pGbpgpwi hwdwuwpq, UbGp 1/wGi/wGbGp pwgwuwl/wG dbwipnpimpjmGGbp: 



6-82 



Upuj^uidp Injhpp ^uquuptqiiulpuG CuipdiiuiQ ShumpjniQ 



1.1 - U]iui^uii|i Q-njh]i]i d-uiiJuiQuil[uiuiui]iui&uij]iQ QUuiiJinJunipjuiQ ^uiijuiuuifiriiiSGhfiii 

£uiQp np iStmp pGqniQmiS hQg np duiiiuiGuilpi U imupui&mpjniQp ppuippg umquipi 3>pqplpiiqui(I hpUmjpQhp jhH, urq 
qpuiGp 2 ulr lk ulu l l l lu ' J bQ ppiup hhui U humqhuuiQnui hG npiqhu iShl[ pQmjpp miupphp qnqiihpp, uiupu huiiiuiduijG 
(pGqqdmiS 1-2)-p, lipiujuiip Injhpp (1 - b)-ni[ uipq\u& huquuphpiulpuG 2uqidiSiuG uiiShGujpGqhuiGnip mqpq h hiulpuqiupd 
dUuiipnpanipjuiQ hiuqMuuuqinuiGhpp iqhinp t iJiQhG q&uijpG U hhuihiupiup qpuiGp IpuQhGuiQ hhinLjuq inhupp. 



Htqpq dUunpnJunipjnLQQhp 

t' = Pi{v)t+ p 2 {v)x 
x' = Y\{v)x + y 2 (v)t 



4,uitpiiquqid dhiuqhnhimpjnLuQhp 
f t = j8i(v')*' + j8i(v')x' 



1.1-1 



(1. 1 - l)-ni[ inpi[iu& dUuiipn[uiSuiQ huiq\uuuipniiSQhpp lihj pnpip uinuiGg Juuiqp U pmiqnq' qnp&uiqpgdhpp qui|m[iu& jhQ n^ 
dmumGmqhg h n^ t^ muqiiudiupjiuQpg: Ujq qnp&iuqpgQhpp qui|m[iu& hG iSpuijQ hunSiuiquiuiujuJuuiQ v h v' mqpq h 
huiquiquipd huqiiuphpuiquiG uqiiuqmpjmGGhppg U hhGg lihp Gujuiuiuiqu t nprytq uijq uiGhuijui qnp&iuqpgGhpp, pGjiqhu Guih 
npn2tq ujjq hpqm huqiiuphpuiquiG uqiiuqmpjmGGhpp iSpjU hquid Ipmqp: Puigp qpiuGpg, pQ^iqhu hphnuS t (1. 1 - l)-n\\ uipq\u& 
dliiuq^npampjuiQ hiui[iuuiupniii(ihppg, Pi(v), P[(v'), f \{v) h Yi( v ') qnp&ui qpg Qhpp ^unpnqiuquiQnipjniQ yuGhG, put} p 2 (v) 
U P' 2 (v' ) qnpdwlqigGhpp mQhG wpwqmpjmG hwlnimmpd jmq^nqmqwGmpjmG L /2(v) h / 2 ( v ) qnp&iu qpg Qhpp mGhG 
uqiuiqmpjuiG ^impnrpulpuGnLpjnLG: 

CQqq&nnI 1-3 - PGuilpuG t bGpuiqpbi np, hunSuiduijG 2 m pddmG huipmpbpwljuiGnipjwG hpiSGwnpnijpp, (1.1 - l)-nd 
mpi[w& iSpw^wip Q-njbpp hwpiupbpwbwG 2uipdiSwG mnpq dbwipnpjmpjwG hmduiuiupnuSGbpp pnpip 
qnp&wbpg-!pniGqgpwGbpp b hwhwnwpd dbwipnpjmpjwG huidwuwpmiSGbpp pnpip hiuiSwuiwmwupiwG 
qnp&uibpg-jjmGljgpuiGbpp inhwp t [pGGG GmjG tymGljgpuiGhpp - GpiujG dp ijhwpmd uijG buip.il/iud wbuip t IpGp v mnpn 
hwpwphpiuliwG wpwqmpjniGpg, pub iSjmu qbwpniiS uijG biupidwd wbuip t IpGp v' hwbiuqiupd hwpwpbpwliwG 
aipiuqnipjniGpg : fimjg wju pGwbiuG GGpwqpmpjmGn, npp ppjmiS t hbGg hwpwpbpwl]wGmpjwG ukqpniGppg, iSbGp 
IpuiqiugmgbGp (1.3) bGpiupmdGmiS: 



(1. 1 - l)-ni[ inpipiifr qfruijpG himpiiuuipnuiGtipp himSiulpDpqhpp npn2p^Qhpp Q2UiQuil}hQp d{v) U d(v') 
inuiniuG2UiQGhpnq', npnGp qui|m[iU(J hQ hunSiuiquiuiujuJuuiliujpuip v U v' mqpq U huilpuqiupd huipuiphpiulpuG 
uipuiqnipjniQQhppg U npnQg uipuiuihujjuinipjniliQtipp IpJiQhG. 

f d(v) = yi(v)j8i(v) - Y2(v)p 2 (v) * 
| d'(v') - Y[(v')P\(v')- Y ' 2 (v')p' 2 (v') * 

(1. 1 - l)-ni[ inpi[iu& mqpq dUuiipnpanipjujQ hiuq^uiuiupniiiQlipp hunSuiqujpqp mi&bmil puui (t,x) uiniuQgpiup4tipp, iSUQp 
quuiuiQuiQp. 



1.1-2 



n(v) , 


P2(V) 


d(v) 


d(v) ' 


P.(v). 


n(v) 



1.1-3 



d(v) 



d(v) 



(1. 1 - 3)-p hunShiSuiintqnq' (1. 1 - ^-nq 1 mp^uift hiuquiquipd dUiudpnJunipjuiQ huiq'uiuujpiSuiQ hhui, iShQp qnpn2bQp 
Juuiqiuq^np qnp&uilipg Qhpp uipimuhujjui4iu& uiQJuuaqujq'np qnp&iuqpgQhpnq^. 



P',(v') 



P' 2 (v') 



ri(y) 

d(v) 

My) 

d{v) 



/i(V) 



r'liy') 



d(v) 
72(v) 



1.1-4 



7-82 



4,iujqiuqiuQ -iuipiuphpiuqiuQiupjuiG ^uiinniq StiunipjniQ 



\>i5uiGiuiqhu (1. 1 - l)-ni[ inpipiifr hiulpuqiupd dUiuipntunipjiuQ hiuiliuuiupniuQupp hiuiSiulpupqp pu&tqnil puui (t',x') 
umiuGgpiupqMjpp, lihGp IpiuiiuQiuGp. 



d'(y') d'(v') 

P'iW) rW) 
d'(y') d'(v') 

(1. 1 - 5)-p hunShiSuiinhpiil (1. 1 - l)-nij uipq\u& mqpq dlauipntumpjiuQ huiq^uuiupiSiuQ hhin, iShQp qnpryhQp uiGpiuiquiipip 
qnpfriuljpg Q hpp lupuiiuhuijuiiliufr Juiuqiuq^ip qnpfriu qpg (I hpnq\ 



Pi(v) = 



Pi(v) 



r[(y') 

cf(v') 

PW) 

rf'(v') 



ri(v) = 



72(v) 



d'(v') 
d'(v') 



1.1-5 



1.1-6 



fqiiup hhin hunShiSiuinhpiq' (1. 1 - 4)-n4 U (1.1 — 6)-nq' uipq\u& qnp&uiqpguQpp wpuiiuhiujuinipjniQQQpp lihGp IpiuiiuQiuGp 
liQinLjiUL umGyiipjmGGQpp, npnQp mqqiuqpnpQG phimu qG q&iujpG dUiuipnhinipjiuG huiuilpupjniGGQppg. 

♦ d(v) U d (v 1 ) npnjfijGbpp hwiSwp rfhGp huiniuGwGp hhwhjwi pGwhiuG wnG^mpjniGp 

d(y)d'{v) = 1 



1.1-7 



♦ ji\ L y\ qnp&wUpgGhpp ilppL mhpp mGp GmL hhmhjmi wnG^mpjmGp 

^i(v)M(v') = 7i(v)r'i(v') 



1.1-8 



t>uq (1. 1 - 4)-ni[ quid (1. 1 - 6)-nq' uipq\u& huiq'uiuuipnHSQhpp hiuuuiqiupqQpp hpqpnpq hiuq^uuiupmuGtipp piudiuGtqnil 
ppuip Ujiiu lihGp IpiuiiuQiuGp lip uipinuihuijinnipjniQ npp lihup Ip^uiGuiqhQp 4i uiumuiU2UiQnil, pdjiqQu gmjg t inpipxid 
uuinpU. 

Hy) P' 2 (y') , 
72(v) y' 2 (v') ' 

(1. 1 - 9)-pg hhinUrmS t np 4i qnp&uiqpgp iSp qtuqpniii iqhinp t quipiq , ui& iJiQp v niqpq huipuipupiulpuu uipuiqnipjniQpg 
puq ujmu qtuqpniiS uijG Ipiipiiluifr iqhuip t IpQp v' hiulpuqiupd huipuiphpuiquiQ uipuiqnipjniQpg, pG^iquu gmjg t uipihjj& 
uuinpU. 

Pi(y) 



= <i(y) 



^-<,(V) 



Yi{v) " IV " y' 2 (v ! ) 

bi hwiSwdwjG (1. 1 - 9)-niJ mpihia& uinQyiipjuiG, 4i(v) U 4i(v') qnptmiqpg-qjniQqgpmGupp ppmp hmijuiuuip qQ. 



<i(v)= <i(v') 



1.1-9 



1.1-10 



1.1-11 



(1.1- ll)-m[ inpipiifr 5>niQqgpnQoq huiiliuuiupniup niGp pu&iSuiG upqni hGuipuiilnpnipjniu. 



iu ) llnwppG hGiupwUnp pit dm Up 



Iv'l = Ivl 



(1.1- 12)-ni[ inpipiifr iquijiiuiGp qtuqpniii piuq'iupiupq'nnS t (1.1 — ll)-ni[ inpiuxifr IpniGqgpnGuiL hiuq'iuuuipniiip, piujg uijG 
huilpiiuniii t uiuQQuipGqhuiQnip dUuupnJunipjuiQ hui^uiuuipniiiuQp quiQtqm (1 - 1-)-ni[ inpiuxifr iSbp iquihuiGjpG: 4,QinUuipuip 
(1.1-11 )-ni[ inpipxifr IpniGqgpnGuiL huiiluiuuipiiuiG iuju uinuijpG hGuipuiq^ip pu&miip iiuGp uhpdniii uGp: 



p) bpbpnpq hGwpwilnp piidniGp 



Iv'l * Ivl 



1.1-12 



1.1-13 



8-82 



Upuj^uiip Injbpp <uipuipbpiuquiQ CuipdiiuiQ SbumpjiuQ 



IIjuhQpQ uiiSbQuipQqhiuGiup dUuiipnpanipjuiQ himpiiuuipnuillhp quiQhpu (1 - 1-)-ni[ uipi[uj& dhp upuhiuQjp puiqMupuipipuii 
t: 4,buibiupuip (1. 1 - ll)-ni[ uipL[uj& $niQqgpnQuq huiipiJuuipnuSp mQp hhinUjiu^ iSpuilj hQiupiuihip pudiuiip. 



<i(v)= <i(v') = <, 



hwuinwinniG 



1.1-14 



lljumpuni[ (11 - 9)-ni[ mpiluj& uinQyupjiuQp, InuiiuiduijQ (1. 1 - 14)-p, iSbQp Ipupnq hQp qphLhhuibjuq b,bpu[. 

Pi(v) _ P' 2 (v') 



<, 



huiuinuiumiG 



/2(v) y' 2 (v') 

£uiQp np y 2 qnp&uiljpgQbpp niQhQ uipuiqiupjuiQ ^unpnquiquiQnipjniQ b rpuuiuqiuQ iSninuiplpiuiQ qbujpniiS, pQ^iqhu 
bpbnuS t (1 - U)-ni[ uipihiifr luiippYpuQ mqpq dbiuipnhaiupjiuQQbppg, qpuiQp mQbQ puiguiuuilpuQ Q2U1Q, pub, p 2 
qnpfriuqpg Qhpp iuQbQ uipiuqnipjuiQ huiquiqiupd jujq'inquilpiiQnipjniQ: ^hinUiupuip (1. 1 - 15)-ni[ inpi[ui& i,\ huiuuiuiuiniQ 
iSbdiupjmQp iSbQp Ipupnq hQp hiuiSbiSimnbL uipbqbpuilpjjQ c lupiuqmpjuiQ hbin h uijq huiuinimniuQp qpb^ hhuihjuq l}bpu[. 



<i =-* 



1 



= hmuuiuiuimG 



flpinbq g-d duiiiuiQiuquiinuipui&nipjuiQ hplipiu^uidiuilpiiQ Ipumugipiifrpp pQmpuiqpnq huiuiniuinmQ iSbdiupjniQ t h npp, 
hiuiSiudiujQ (1. 1 - 15)-nL[ mpOjUift lunQyiipjiuQp, prnnp pQbpgpuq huiiiuil4iupqbpnui mQp GmjG iSbdmpjiuQp h ul}qpniQpnphQ 
quipnq t LpQhL h qpuilpuQ b piugiuuiuquiQ iSbdmpjiuQ: 

(1. 1 - 16)-ni[ inpipiifr 4,i qnp&uiljgp uipdbpp uihquiqpbpiq' (1. 1 - 15)-nL[ uipOjUift lunQyiipjiuQ dbg, iSbQp p 2 
qnp&iuqpg-^niQligpiuQhpp Ipupnq hQp uipinuihiujinhL y 2 qnp&iuqpg-^niQligpiuQhpnq' hhuihjuq b,hpu[. 




1.1-15 



1.1-16 



1.1-17 



lIjQmhhinh fi 2 qnpfriuqpg Qhpp uipiniuhiujinnLpjmQQhpp (1. 1 - 17)-pg inhrpun.phpii[ (1. 1 - 2)-h lihg QhQp npn2p^Qbpp 
hiuiSiup quuiujQuiQp hhuihjuq wpuiuihuijuiiupjniQQhpp. 

d(v) = n(v)j8i(v) + g\[Y2(v)] 2 * 
c 

d'W) = y[(V)p\(v') + s4[ri( f ')] ! * 

c 

\>i5uiQuiiuhu p 2 qnp&uiljpgQhpp wpuiuihuijuinipjniQQhpp (1. 1 - 17)-pg uihqiuqphpiq' (1. 1 - l)-p iSbj, QhQp iSpiu^unp 
Q-njbpp huipiuphpuilpjjQ 2iupdiSiuQ mqpq b huilpurpupd dbunpnJunipjniQQhpp huiiiuip IpnnuiQujQp hhinUjuJL himliuuuipnuiQhpp. 



1.1-1! 



fluipq dUuiQintuiupjniQQhp 

= Pi(v)t-g J T y 2 (v)x 
c 

' = y\{v)x + y 2 (v)t 



4,uitpiiquipd dbunpnJunipjniQQbp 

t= P\(y')t' -g\y' 2 {v')x 
c 

x = y[(v')x' + y 2 (v')t' 



1.1-19 



CQqq&nnI 1 -4 - (1.1 - \&)-nd inpdmd dhmdmJumpjmG d(v) h d'(v') npnjp-jGbpp-, hwrfwdwjG (1.1 -l)-p, 
apwdwiSwGwl] ujbuip t ifiGbG GuiiS qpiubwG b buiiS t[ pwgwuwbwG iSh&mpjmGGhp: IpwhwG hmii pwgwuwhuiG npn^pt 
niGbgnq dhwipnpjmpjmGGbpp tlpw^wip muipwdnipjuiG iShp, hwtluiduijG (1 - Q)-nd b (1 - fc)-/7(/ wpGiud uwhiSwGmiSGbpp, 
dbGp qpwGp GmjGujbu huiGGiuGbGp hwiSwuiwmwupjiuGwpiup <aipwhwG dbimpn[unipjmGGhp» buiiS «pwgwuwbwG 
dbwipnpjmpjniGGbp»: Uju bphm npiubwigbu mwppbp dbiuipnpjnipjmGGhpG t[ niGbG qnjmpjwG ppwdmGp, npndhbwb 
qpmGgpg uiiSGG iSbbp Glpupmqpmd ' t dp npnjuibp jtpqJihiubuiG bpbnijp: 



^puiquiQ dbuiqhnhanipjmQQhp 

J d(v) > 
1 rf'(v') > 



PuiguiuuiljuiQ dbuiq*inJunipjmQQbp 

J d(v) < 
I d'(v') < 



1.1-20 



9-82 



4,uijlpxiquiQ -iuipiuphpuilpuQnipjuiG ^imnnilj ShumpjniQ 



1.2 - I^Qh]ig]iui^unJuil[ui]iqh]i]i UqqpGuilihuih]i]i GuifichJuiG ^huiuiqnuiniiSii 

\>uiju Q2hQp, np uinuiQg pGqhiuQpnipjuiQ qDii liDnuiG^Qpu, iSpiu^unp iniupiufrnipjiuQ lihg K pGhpgpuiL himSuilnjipqp 
QquiuiiSiuiSp K' pQhpgpun hunSiuliuipqp 2iupdiSiuQ v uipuiqmpjniGp (ninjm uipuiqmpjniGp) iSbQp Ipupnri hQp pQinph^ uijQiqhu 
np uijQ dp2in ninrppiifr it 1 ^ X uiniuGgpp qpiuquiQ ninrpupjunip U hDinUuipuip iujQ IpiiGp lyiuilpuG lih&nipjniG: 



v>0 1.2-1 



lljdii oquiq'hpiq' (1. 1 - 19)-n4 uipu\u& lipiujuiUi Injhpp hiupiuphpuilpiiG 2iupdiiuiG ninjm U hiulpurpupd dliiuq^npinipjiuQ 
hiui[iuuiupniiiQhppg, gniguiphptiGp ^pqplpuquiQ uninhgnui L hui2ilaG]2 K' U K pGhpgpuiL huiiiuilpupqtipp uqqpQuiqhuihpp 
2UipdiSuiG uipiuqnipjniQQhpp, npnQp iqhuip t hiuiipQqQhQ hoGg GmjG pQhpgpun hunSuiquipqhpp hunSuiiqujuiujuJuuiQ 
hiupiuphpuilpiiG lupiuqnipjniQQhpp hhin: 

1 . K pGbpgpwi hwtlwljiupqli GbwmtlwUp K' pGbpgpwi hwiSwbwpqp uuqpGwbbwp 2wpddwG 
hbmwqnmm dp 

K' pQhpgpuiL hunSuiquipqp O' uljqpGuilpjinp 2iupdiiuiG pGinpnipjuiG nfciqpniiS, iujij ul}qp Quil[tiinp uiuipui&uilpuQ 
uinuiQgpuipq'hpp K' U K pGhpgpuiL huniuilpxipqQpniu' IpiiGhGuiG htunLjuiL uipdhpQhpp. 

= ° 1.2-2 

= vt 

(1.2 - 2)-ni[ inpipufr O' ul}qpQuil}hinp uiuipui&uilpiiG uinuiGgpuipilGPP uipdhpQhpp inDrpunjiDpiil (1. 1 - 19)-ni[ inpipufr 
inuipiufriuquiG umuiGgpuipdJi nu]pq dUuiqhnpimpjujQ hiuipuuiupiiuiG iSq$>, lihGp quuiuiGuiGp y 2 qnp&iuqpg-J>niQl}gpuijp 
uipiniuhuijinnipjniGp. 

y 2 (v) = -yi(v)v 1.2-3 

lljdii tl (1.2 - 2)-nil uipu\u& O' uqqp Quil}huip iniupiufriulpuG uinuiGgpuipdJjpp uipdhpQtipp uiDnuinjiQpiq' (1. 1 - 19) -ml 
inpipufr diuiSiuGuiljp U uiuipui&nipjuiG uiniuQgpujpq'tipp hiulpurpupd dUuiq^npimpjiuQ himpuuuipnuiQDpp iSbj U uijq 
himpiiuuipniiiGDpp piudiuQUpiil ppuip i]pui, iSUGp IpnnuiGuiGp v mnjiq huipuipQpiulnjjQ uipuiqmpjuiG uipuiuihuijuinipjniGp. 

v=i = 4^ 1-2-4 

2. K' pGbpgpwi hwiSwbwpqp GbwmiSwiSp K pGbpgpwi hwiSwbwpqp uhqpGwhbinp 2wpdiSwG 
hbmwqnmm dp 

K pQhpgpuiL huniuilpxipqp O ul}qpQuil}hinp 2UjpdiiuiQ pGinpnipjuiG nhujgnul, uijij ul}qpQuil}tiinp uiuipui&uilpiiG 
uinuiQgpiupq'tipp K U K' pGtipgpuiL huniuilpxipqQpniu' IjniGhQuiG hbuiUjuil uipdhpQhpp. 

1-2-5 

x — v t' 

(1.2 - 5)-nil inpipufr O uqqp Quil}huip iniupuifruilpuG uinuiGgpuipdJjpp uipdhpOtipp uiDnuiqpapiq' (1. 1 - 19)-nil mpOjUift 
iniupiu&iuquiQ uinuiQgpiupq'p hiuquiqiupd dUuiq^npimpjuiQ hiuiluiuiupiiuiQ iShj, lihGp quuiuiQuiQp y' 2 qnp&iulipg-5)niQl}gpuijp 
uipinuihuijinnLpjniQp. 

y'i(v') = -ri(v')v' 1-2-6 

lljdii tl (1.2 - 5)-nil uipOjUift O ul}qpQuil[hinp muipui&ujl}iuQ uinuiQgpuipiltipt lupdhpQbpp inhmunjiDpiil (1. 1 - 19)-nil 
inpipufr dunSuiQujl}p U imupui&mpjuiQ uinuiQgpujp4opp ninjiq dUuiqhnpinipjuiQ hunliuuuipniiiQtipp iShj U uijq huid 1 ujuujpnnSQtipp 
puiduiQhpiil ppuip djiui, lihQp quimuQiuQp v' huil}iurpupd huipuiphpiulpuQ lupiuqiupjuiQ lupuiuihuijuinipjniQp. 

v' = 4 = ^w 12 . 7 

t' 01 (v) 



10-82 



U|iuj^uh}i Injhpp <uipuipbpiuquiG CuipdiiuiQ ShumpjniQ 



UjQiuhbinL (1.2 - 7)-p iSb$> intarpuqphpi^ (1.2 - 3)-ni[ npr^uifr Y 2 ( v ) c l n Pfr u ' 1 'l9P uipimuhuijuinipjniQp, iSbQp IpnniuQuiGp 
v' hiulpurpiipd huipuiphpiulpjjQ uipuiqiupjniGp uipiniuhiujinU 1 ui& v niqpq hiupuiphpuilpiiG uipuiqnipjuiiip. 



riO) 

iSi(v) 



(1.2 - 8)-pg iSbQp IpnniuQuiGp QuiU hhmlijuq uinGyupjiuGp. 

7l(v)v = -ySi(v)v' 

"bihuQimqhu (1.2 - 4)-p lihg uihquiqpbpiq' (1.2 - 6)-nq' npn2qMjj& y 2 (v') qnp&uiljgp uipiniuhiujinnLpjniGp, lihGp 
quuiiuGuiQp v niripq hiupiuptipuil}uiQ uipuiqnipjniQp iupuiuihuijim[iu& v' hiuqiuquipd hiupiuptipuil}uiQ uipiuqiupjiuiip. 



r'i(y') 

/J'i(v') 



(1.2- 10)-pg iSbQp IpnniuQuiGp QuiU hhuiUjuq lunGynpjmGp. 

y'i(v')v' = -/3i(v')v 
(1.2 - 3)-ni[ U (1.2 — 6)-ni[ npn2ipn<* / 2 -ti U y 2 -p uipuiuihuijuinipjniQQhpji uibnuinpbinil (1. 1 - 17)-ni[ inpipnfr jit 
qnpfriu qpg G hpp uipiniuhiujinmpjmGGhpp lihg, iSbQp IpnniuQuiGp hbinUjuiL uinGynpjnLQGhpp. 



Mv) = g-^n(v) 



j8i(v') - *-Vri(v') 



\ji5mGiuiuhu (1.2 - 3)-ni[ b (1.2 - 6)-ni[ npn2ipnfr ^'P ^ /^"P mpuiuihuijuinipjniGGbpp uihquiqpbpiq' (1. 1 - 18)-nL[ 
inpipnfr npn2p^Qhpp uipuiuihuijuinipjniGQhpp iShj, lihQp IpnniuQuiGp hhmhjuq uinGyiipjnLQGhpp. 



rf(v) = ri(v)[pi(v) + *^-ri(v)]*o 
«*V) = ri(v')[j9i(v') + *-^-ri(v')] * o 



lIjGnihhinU (1.2 - 13)-p iSh$> l^ppumhpul (1.2 - 9)-p U (1.2 - ll)-p uipinuihuijinnipjniGGhpp, lihQp npn2p^Qbpp huiihup 
IpnniuQuiGp QuiU hhinUjuq hunSuijunp uinGynpjnLGGhpp. 

«/(v) = ri(v)/Mv)(i-*-^) *« 



< 



^'(v')-7 , 1 (v')i3' 1 (v , )(l-g^) *0 



1.2-8 



1.2-9 



1.2-10 



1.2-11 



1.2-12 



1.2-13 



1.2-14 



f*uq (1.2 - 3)-m[ U (1.2 - 6)-ni[ npn2ihufr y 2 'P ^ ^2'P uipuiuihuijinnipjni.GGbpn uibnuiqpbinil QuiU (1. 1 - 19)-ml uipijuid 
huipuiphpuiquiG 2iupdiiuiQ mnjiq U huilpuquipd dUunpnpimpjniGGhpp iSh$> iJhGp quinuiGuiGp hhinbjuq hunluiuuipnuiGhpp. 



fliqpq dUunpnpinipjniGGhp 



ji(v)(x-vt) 



<uiquiquipd dUunpnpinipjniGGhp 

t= p\{v')t' + gy\{v')^ T x' 
c 

x = y\(v')(x' -v't') 



1.2-15 



M^iqbu QuiU (1.2 - 15)-p dbg qhpuinbpi4 (1.2 - 9)-p U (1.2 - ll)-p uipuiuihuijuinipjniQGhpp, iSbQp huipuiphpuilpuQ 
2iupdiSuiG mqpq U huiquiquipd dhunpnpinLpjniGGhpp huiiiiup quinuiGuiGp Guih hhmhjuiLhiinhuuuipnuSGhpp. 



Hiqhq dhuiq'inhinipjniGGhp 
t' = Pi(v)(t-g^x > ) 

*' = yiiy)(x-vt) 



4,uitpnquipd dhunhnhinLpjniQGhp 

* = j8'i(v')(*' " *-£*') 

x = 7i(v')(x' - vY) 



1.2-16 



11-82 



4,uijqiuquiQ -iuipiuphpuiqiuQnipjuiQ ^imnmq ShunipjniQ 



1.3 - ^uipuiphpuiljuiQriipjuiQ ^]iiSQuiri : ]inijp]i Oqtnuiqnp&nLiSii 

^uipuiphpuiquiQ GuipchSuiG £)Luup.npjnipjuiG ^uii]uiuuipniiSGhp]i Uh^ 

^uipuipDpuiquiQnipjuiG hpiSGuiqpnijpp qppiunhpu huiiiuip lihQp iqhuip t oquiqMiQp (1.2 - 15)-ni[ uipq\u& 
huipiuphpujl}uiQ 2uipdiiuiG niqpq U hiuquiqiupd dUiuipnpimpjuiQ hiui[iuuiupniiiQhppg: 

1 . K pGbpgpwi hwiSwl]iupqIig, l]iuiSwjwl]iuG t uiwhpG, hui20bGp K' pGbpgfiwi hwiSiubwpqp GlpiimiSwiSp 
hwGquinfi dptiwhmiS quiGGnq L /o bpbwpmpjniG niGbgnqp dnqp bpbwpmpjniGp: 

Uju qhiqpniiS, lihq huiiiuip hhimuppppnipjniQ QUpquijuigGnq uinuiGgpuipqMjpp IpuGUGuiG htunLjuq uipdhpGhpp. 

H-t\ = 

xi-xx = I 1.3-1 

X 2 - x\ = /() 

(1.2 - 15)-nil inpq^ufr iniupiudnipjiuG rnqjiq dlampnpiiupjiuG huaqMinRupiSuiG lihg uihqujqptipiq' (fi,xi) U (t 2 ,xi) 
uinujGgpiupqMjpp, iShGp quiniuGuiGp inuipiudiulpuQ x\ U x' 2 uinuiQgpiupqMjpp. 

x[ = n(v)(JCi -vfi) 3 _ 2 

x 'l = Yi( v )( x 2 - vt 2 ) 

Uj QiuhtunL oquiqljpiq' (1.3 - 2)-pg U (1.3 - l)-nij uipq\u& iunuiQgpiupi[tipii lupdhpGhppg, hui2qMjGp K 1 pGhpgpuq 
himSiuqujpqniu' uiQ2iupd quiGGnq dnqji hplpjjpnipjniQp, npp huiq\uuujp iqhinp t LpGp ^o-p- 

x' 2 -x'i = / = Yi(v)[(x 2 -Xi) -v(t 2 -fi)] = f\{v)l 1.3-3 

K pQhpgpuqhuiiiuil}iupqp uihuuiQlijnLQpg uijq 6nqp hpquipmpjuiQ U K' pGhpgpuq hiuiiiuqiupqniu' huiQquinp 4p6uiliniii 
qinGq^iq QmjQ dnqp hpquipmpjuiG hiupiuphpmpjniGp iSp2Ui iqhinp t IpQp qpuiqiuG iShdnipjniG h himSuidiiijG (1.3 - 3)-p, uijQ 
ql hGh. 

4- = — r- > 1.3-4 

«o 7\{v) 

2. K' JiGbpgpwi hiuiSiulpiipqpg , IpiitfwjwlpiiG t' iquihpG, hw2dbGp K pGbpgpmi hwtiwbwpqfi GhwuiiSwiSp 
hwGquinfi Gpduibnid qmGUnq b GmjGujbu la bpbwpmpjniG mGbgnqJi dnqp bpbwpmpjniGp: 

Uju qhiqpmiS, lihq huniiup hhmiuppppnipjniG GhpqiujuigGnq uiniuGgpiupqMjpp qniGhGiuG hhinhjuq lupdhpGhpp. 

4 -t\ = o 



Al X, i — I 

X 2 -X\ = /() 

(1.2 - 15)-ni[ inpipiifr inuipuifrnipjuiG hiuquiqiupd dUunpnJunipjuiQ hinqMiiuiupu'iiiG lihg inhqiuqphpiq' (t\,x\) U (t' 2 ,x' 2 ) 
uiniuGgpiupqMjpp, iShGp quiniuGuiGp inuipuifruiquiG X\ h x 2 iuniuQgpiupU_hpp. 

J xi = r\(v')(x\ -v't[) 
I x 2 = y\(v')(x' 2 - v't 2 ) 



1.3-5 



1.3-6 



llj QmhtiinU oquii[tipiq' (1.3 - 6)-pg U (1.3 - 5)^4 mp^uift iunuiQgpiupi[tipt uipdhgQhppg, hui2iltiQp K pQbpgpuq 
hunSiuquipqimS uiQ2Uipd qinQLjnq dnqp DpquipmpjniGp, npp huiOjUiuuip iqhinp t l]iGp /o-Ji. 

X2 -xi = l = r\(v')[(x 2 -xi) - v'(4 - t[)] = y\{v')l' 1.3-7 

K' pQhpgpuq hunSuiquipqp inhuiuQqjniQfig uijq dnqp UpqiupnipjiuQ U K pQhpgpuq huniuiquipqnLii huiQquinp q'pduiqniii 
qinQq'nq QmjQ dnqp hplpupnipjiuQ huipuiphpnipjmQp iSp2Ui iqhinp t iJiQJi qpiuquiQ iSh&nipjmQ U hunSiudiujCi (1.3 - 7)-p, uijQ 
q^lQp. 



12-82 



Upui^uup Injupp ^uipuipupuilpiiG CuipdiiuiG ShumpjmG 



/o 



rl(v') 



> o 



1.3-8 



■{uiuuiduijG (1 - P)-ni[ inpipufr hpuQuinpmjpGapp uinuigpG uliqpniQgp* huipuipupuilpuGrupjuiG uljqpiuQpp, K U K 1 
pGupgpuq huiuuilpupqhpp uiauuiGlijmGpg npinuiplppu& U huiuuiupuinuiutuuiQuipuip (1.3 - 4)-niJ U (1.3 - 8)-niJ uipihij&, 
2Uipdi[nn u uiG2Uipd upuGmjG dnnp QplpiipmpjmGGQpp huipuipupmpjmGGQpp, ujhinp t LpGhG GmjG JpmGljgpuiG, upuijG up 
qhiqprmS uijQ ljuj]m[iU(J iqhuip t IpQp V mqpq huipuiphpiulpuG uipuiqmpjmGpg, pulj iSjnm ntuupnuT v' huilpurpupd 
hiupiuphpuilpiiG uipuiqmpjmGpg, uijupGpG ujhuip t uihnp mGhQui hauiujuq uinGyupjmGp. 



ri( v ') = 7i( v ') 



Puijg puiGp np, uiuhGuipGrpnuGmp nauipnui, huiuuiduijG (1.2 - 8)-p Ipuii (1.2 - 10)-p, Iv'l * Ivl hhuiuuipuip. 

ri(v') * n(v) 



1.3-9 



1.3-10 



Cun.q&mu 1-5 - £mGp np bwGmjwbmG hwpwpbpiubiuG wpwqnipjuiGp ^wpdilnq guiGbiugwd bpbm pGbpgpwi 
hwGwhwpqp mbmiiGhjmGpg 2iupdi[nq dnqp L hwGqump itbp qmGdnq GmjG dnq/i bphwpnipjmGGbpp hmpmpbpnipjniGp £p 
biupnq ipGbi pwgiuuwbwG iSh&mpjmG, hbmbiupwp (1.3 - 4)-/z U (1.3 - S)-fi, pG^igbu Gwb (1.3 - 9)-p wpnjmGpGhppg hhwhmiS 
t np y qnpdwbpg-tymGbgpuiG iSpjin u/binp t IpGp qpwbmG dbdmpjmG: 



n(v) >o 
ri(v') > o 



1.3-11 



3. K' pGbpgpwi hiuiSwlpiipqmiS, mwpwdmpjwG iSpbGmjG x' dwjpmd mbq[i t niGbGnid rffa pud hujjmGfi b 
upupphpiupwp bpbGdnq upumwhuip, npfi apuppbpmpjwG mUnqmpjniGp to t: 4w2dbGp mjq igwuiwhwpfi 
apuppbpmpjwG uibnqnipjmGp K pGbpgpwi hwdwbwpq[i whuiuGbjmG[ig: 



Uju nuuipmu, lihq huiuuip hauiuippppmpjmG GhplpujuigGnn uiniuGgpuipq'hpp IpuGuGuiG htunLjuiL uipdupGapp. 

t' 2 - t\ = t > 
x 2 — x\ =0 
ti - h = t 

(1.2 - 15)-ni[ inpipufr duiuuiGuiljp huilpumupd duuupntumpjuiG huiipiiuuipuuiG lihg uiamumiQmil (t[,x\) U (t' 2 ,x' 2 ) 
umuiGgpuipiltiPD. uuGp IpnnuiGuiGp duiuuiGuiljp t\ u t 2 uinuiGgpuipi[Qpp. 

fi = P',(v')t[+gY'i(v')\x\ 
c 

ti = P\{v)t' 2 + gy\{v')\x' 2 
c 

lIjGmhtunu oqim[bl_nq' (1.3 - 13)-pg U (1.3 — 12)-nil uipilui& uinuiGgpuipiltipp uipdapGuppg, hui2iltiGp uijn puq 1 huijuiGp 
upiiuiuihuipp upuppapmpjuiG inLnnmpjmGp K pGhpgpuq huiuuilpupqp uiauuiGlijmGpg. 

H-h =t= P\(v')(t' 2 -t\) + gY[(v')\(x' 2 -x[) = P\{v')to 

c 

K pGupgpuq huiuuilpupqp uiauuiGljjmGpg uijq pi[ huijuiGp upuinuihuipp upupphpnipjuiG uiunnmpjuiG U K' pGhpgpun 

huiuuiljuipqniu huiGquuip ilpiSuiliniu quiGiJnq GrujG ujuiuiuihuipp uuuppapmpjuiQ uiUnqmpjuiG huipuiphpmpjniGp, huuSuiduijG 

(1.3-14)-p, IpjiGp. 



1.3-12 



1.3-13 



1.3-14 



fo 



- /W) 



1.3-15 



13-82 



4,uijlpulpiiQ -iuipuiphpuilpuQiiipjuiG ^uiuimlj ShunipjniQ 



4. K pGhpgpwi hwtfwljiupqniit, iniupw&mpjwG tlpLGmjG x dwjpmiS uibqp t niGbGnitS Gwpjnpq [iud hwjwGp 
L wwppbpwpwp hpbGUnq upuwwhwpp, npp wwppbpmpjwG mhnqmpjniGp to t: 4w2dbGp mjq wwmwhwpp 
upupphpmpjiuG mbnqmpjniGp K' pGhpgpwi hwdwhwpqp mbuwGhjmGpg: 



llju nhiqpniu', lihq huuiuip hDuiuippppnipjniG QhplpiijuigGnq uinuiGgpuipqMjpO IpiiGhGuiG htnnujuq uipdhpQhpp. 

ti-h = to > 

X2 — Xl =0 

t' 2 - t[ = t' 

(1.2 - 15)-ni[ uipipufr duiiSuiGuiljp mqpq duuiipnpimpjuiG huiipuuuipiSuiG lihg uiDquiqpQpiq' (fi.xi) U (t 2 ,x 2 ) 
lunujQgpuipilhpp, iShGp IpiuiuiGuiGp duiiSuiGuiljp t\ u t' 2 uinuiGgpuipiltipp. 

f, = Pi(y)ti+gri(y)-^-xi 
c 

t 2 = Pi(y)t 2 + gYi(y)^ : x2 
c 

Uj GmhQinU oqim[bpiLl (1.3 - 17)-pg U (1.3 — 16)-nil uipipu& uinuiGgpuipiltipp uipdhpOtippg, hu^GJjGp uijq put) huijuiQp 
iquiuiuihuipp upupphpnipjuiG inhnqnipjniGp K' pGhpgpuq huiiSuiUuipqDpp inhuiuQqjmQpg. 

t' 2 -t\ =t' = j8i(v)(»2-»i) = P\{v)U) 
K' pGhpgpuq huiiSuilpupqp inhuiuQqjniQpg uijn puij huijuiQp upuuiuihuipp upupphpnipjuiG inLnqnipjuiG h K pGhpgpui^ 
huiiSuilpupqniiS huiGquuih OJuSuilpiiiS qinGipiq GmjG upuuiuihuipp uiuipphpnipjuiQ inUnqnipjuiG huipuiphpnipjniGp, huiiSuiduijG 
(1.3-18)-h, ql hGh. 



1.3-16 



to 



- Pi(y) 



1.3-17 



1.3-18 



1.3-19 



\>nijGiqbu huiiiuiduijQ (1 -P)-ni[ uipipuft hhiiGuiqpnijpGhpp uinuijpQ ulpnpniQpp* huipuiptipuil}ui(inipjuiQ ul}qpniQpp, K 
h K' pGhpgpuq hiuiiiutpiipqhpp uihuuiGtjjniGhg qhinuiptphu& u huiiiuiupiiinuiupiiuGuipuip (1.3 - 15)-niJ U (1.3 - 19)-ru[ 
uipi[ui&, lipLGnijG huijuiGh iquiuiuihuipp upupphpnipjniGGhpp huipuiphpnipjniGGhpp, iqhuip t ihGbG GmjG 3>niGlpjhuiG, lihuijG 
lip qhuipmii uijQ l}uipiilui& ujhuip t iJiQp v ninjiq huipuiphpuilpiiG uipuiqnipjniQpg, Jiuq lijniu nhiqpniiT v' huilpuquipd 
huipuiphpuilpiiG uipuiqnipjniQpg, uijupQpQ iqhuip t uihqh niGhGui hhuihjuq uinGyiipjniGp. 



P'i(v') = Pi(v') 



Puijg puiQp np unStiliuipQqhuilinip nbiqpniiS, huiiiuiduijG (1.2 - 8)-h l}uuS (1.2 - 10)-p, Iv'l * Ivl hhuihuipuip. 

Pi(v') * J8i(v) 



1.3-20 



1.3-21 



Cuqq&nid 1 -6 - /? i qnp&whpg-$>niGhgpwjp G^wGp iSwupG wniujdU dbGp n^pG^ huimiih jqpwbGp: Ujq hwpgp 
GbppGwbwG wwmwupjwGp dbGp bumwGiuGp hhuiwqiujmiS: 1-pw hwdwp dbGp Ipupnq bGp hwumwmbi dfiwjG hbmhjwip. 



j8i(v)*0 
j8i(v')£0 



1.3-22 



lIjGnihhinU (1. 1 - 8)-nil uipipuft uinGyiipjuiG lihj lippuinhpiij (1.3 - 9)-p U (1.3 - 20)-p uipqjniQpQhpp, iSbQp IjuuiuiQuiGp 
hhuiUjuq uinQjiupjiuQp, npp huiiiuiduijQ (1.3 - ll)-p iip2Ui ujUuip t IpQp qpuiliuiQ lih&nipjniQ. 



Pi(v)Pi(v') = yi(v)y 1 (v')>0 



1.3-23 



Cun.q&nul 1-7 - (1.3 -23)-nrf inpGmd uinG^mpjmGp, hwrfhGuijG qbupi, iShq fimjmif t np bpb KUK pGbpgpwi 
hwilwhwpqhpp mbuwGhjniGpg hhwwqnwrfmrf t rfpbGmjG $pqpbwhwG hphnijpp, uiujiu ySi qnpdwupg-!pniGhgpwjp GjiuGp 
hphm pGhpgpwi hwtSwhwpqhpmi! t[ iqhinp t IpGp GmjGp ' IpiiiS qpwbwG b buitS t[ piugmumbwG: 



14-82 



Upui^uiQi Injhpp <uipuiphpuilpjiQ CuipchiuiQ ShumpjmQ 



Ujchi oquiqMimq' huilpxiquipd uipuiqnipjuiQ (1.2 - 8)-m[ inpipiicJ puiQuidhhg U (1.3 - 23)-nq' uip^uift uinQyupjniQpg, QhQp 
Ipjjpnq hQp gmjg inuqnp v' huilpjiquipd uipuiqnipjuiQ huiquiquipd uipuiqmpjniQp qui QmjQ v mqpq uipuiqmpjniQQ t, 
uiQquipi uijQ puiQpg dhuiqinhimpjmQp qpuiquiQ t ph puiguiuuilpiiQ: 



(V') -v 



(1.2 - 10)-p lihg Ijppuinhmq' (1.3 - 9)-p h (1.3 - 20)-p uipqjmQpQhpp, QhQp niqpq huipuiphpuilpiiQ uipuiqnipjuiQ huiiiuip 
quuiuiQuiQp hhuihjuq uinQyiipjmQp. 

J3i(v') 
(1.3 - 25)-pg iShQp IminuiQuiQp Quih hhuihjuq uinQyiipjmQp. 

Yi(v')v' = ~P\{v')v 
(1.2 - 6)-p U (1.2 - 12)-p iShj qppujnhpi^ (1.3 - 9)-p uipqjniQpp, iShQp l}huiiinq4bQp np jit h Y 2 hiuiquupip h uiQhiuiq 
qnpdui qpg Qhpp iqhinp t LpQhQ QmjQ IpmQlighuiQ, iShuijQ tip qhiqpniii uijQ quihiq\u& iqhinp t ihQh v mqhq huipuiphpuilpiiQ 
uipuiqmpjniQ[ig, puq iSjmu qtuqpmiT v' huiquiquipd hiupuiphpuiquiQ uipuiqmpjniQJig, uijufiQpQ uihqh niQh hhinhjuqp. 

y'i(v') = Yi(v') = -ri(v')v' 

j8' 2 (v') - j8 2 (v') = gri(v')4 
c 

UjQmhhinh (1.2 - 13)-nil uipijuift npn2pjQhpp iSh$> Ijhpumhmil (1.3 - 9)-h h (1.3 - 20)-h uipqjmQpQhpp QhQp IminuiQuiQp 
hhuihjuq uinQyiipjmQQhpp. 

rf(v) = ri(v)[^i(v) + m(v)^-]*o 

rf'(v , ) = ri(v , )[j8i(v') + gr.(v , )^ 2 i ]*o 

(1.3 - 28)-pg hhuihmiS t np npn2pj-J>niQh.ghuiQhpp huuSuip uihnp niQh hhuihjuqp qSniQlpghnQuq uinQyiipjmQp. 



rf'(v') = rf(v') 



<hinhuipuip (1.1- 7)-m[ uipipiifr uinQyiipjmQp l}qp4p hhuihjuq Iphpiq. 



d(v)d(v') = 1 



f»ul} (1.2 - 14)-m[ uipihiifr npn2p^Qhpp lihj QmjQiqhu qhpuinhmi[ (1.3 - 9)-h h (1.3 - 20)-h uipqjmQpQhpp, pQjujhu Quih 
(1.3- 29)-p, QhQp dhuiipnhimpjuiQ npn2p^Qhpp huiiiuip IminuiQuiQp Quih hhmhjuq uinQyiipjmQGhpp. 



< 



«*(v) = 7i(v)j9i(v)(l -*-*£) *0 

rf(v , ) = n(v , )^i(v')(i-g^r)* 



(1. 1 - 4)-m[ inpipiifr hun[uiuuipmiiQhpp huuSuilpupqhpp uinuijpQ huu[uiuuipniiiQhpp iSh$> U_ppuinhmi[ (1.3 - 9)-p h 
(1.3 - 20)-h uipqjmQpQhpp, pQ^ujhu Quih (1.3 - 28)-p h (1.3 - 31)-p uinuijpQ huiq'uiuuipnuSQhpp, lihQp IpiuuuQuiQp hhmhjuq 
hplpii uinQyiipjmQQhpp. 

/i(v) 



/W) 



n(v') = 



«*(v) 



/Si(v) 



1 

/»i(v) + «n(v)-4 



ySi(v) 



1 



0i(v) 



0-^) 



rf(v) n(v)[j8i(v) + «n(v)-^-] n(v)(i-g^) 



f»ul} (1. 1 - 6)-m[ inpipiifr huu[uiuuipmiiQhpp huuSuilpiipqhpp uinuijpQ huu[uiuuipmiiQhpp iSh$> QmjQiqhu lippuinhmq 1 
(1.3-9)-h, (1.3-20)-lih (1.3 -29)-h uipqjmQpQhpp, pQ^qhu Quih (1.3 - 28)-h U (1.3 - 31)-p hplmnpq huu[uiuuipmuQhpp, 
QhQp IjuuiuiQuiQp hhmhjuq hplpu uinQ^mpjmQQhpp. 



1.3-24 



1.3-25 



1.3-26 



1.3-27 



1.3-28 



1.3-29 



1.3-30 



1.3-31 



1.3-32 



15-82 



4,uijlpxiquiQ -iuipiuphpuilpuQnipjuiQ ^imnmAj ShunipjniQ 



0i(v) 



7iO) = 



1 



1 



ri( v ') = 

d{V) /»i(v') + «ri(v')-^- /»i(v')(i-*-^-) 

J8i(v') jSi(v') i 



1.3-33 



d(v ' } n(v')[pi(v') + «n(v')-^-] r.(v')(i-g^) 

<p2hl_nil (1.3 - 23)-p, iShQp (1.3 - 32)-pg Ipuii (1.3 - 33)-pg lpupni\ hQp uuiuiQunhhuiUjunhujiiuj^unp uinQynpjniQp. 



n(v)ri(v , ) = /Ji(v)/Ji(v , ) = 



Pi(y) 



01 (v') 



l 



PiOO + mOO-V j8i(v') + m(v')-^ 



> o 



l_ g : 



1.3-34 



■EuiGp np, huniuiduijG (1.3 - ll)-p, yj(v') U /j(v) qnp&iulipgQhpp iSp2in qpiulpud iShdnipjiuG dG, hhuiUiupiup 
(1.3 - 32)-p U (1.3 - 33)-p uinuigpQ huii[iuuuipniii(itippg hhuilinid t np ySi(v') U /?i(v) qnp&iul}pgQhpp Q2iuQp ljuj]m[iu& t 
CipuijG J(v) U <i(v') npn2pjQhpp Q2iuQpg lipiujQ: <p2hpiil QiuU (1. 1 - 20)-p, lihGp lyiuilpuQ U piuguiuiulpuG 
dUujipn[unipjniQQtipp Ipupnq hGp uiuMuiGql QiuU hQinLjuiL qhpu}. 



^piulpuG dUuiipnhinipjniQQhp 

r Piw>o 

1 0i(v')>O 



PuiguiuuiljuiQ dUuiihnJunipjniQQhp 

f ySiW<0 
1 J8i(v')<0 



1.3-35 



OquiqMipiq' (1.3 - ll)-pg U (1.3 - 35)-niJ uipqMjjft qpiulpuG U piuguiuiulpuG dUunpnJunLpjniQQhpp ntnqpnul /?i 
5>niQl}gpui-qnp&uiligp Q2UiQQhppg, pGjiqhu QiuU oqinq , hpii[ (1.2 - 8)-ni[ inpipufr hiulpurpupd hiupiuphpuilpiiG uipiuqnipjujG 
piuQuidlipg, iSUGp l}iupni\ hGp lpirpSGnpn24til mjil uipuiqnipjuiG Q2iuQp hiupgniiS Uu hhuiUjun IjUnuj. 



f l-piulpuQ dhuiipntunipjniGGDp 



PuiguiuuiljuiQ dUuiq*inJunLpjmQQhp 



PlOO 



v < 






v > 



1.3-36 



CQiiq&nnI 1-8 - (1.3 -36) -fig hhuibmiS t np qpiubwG dbwipnpjmpjmGGbpp qbiqpmit hiubwqwpd wpwqmpjniGp 
qmnGnni t hwbwqpp lupwqmpjmG, fiub pwgwuwbwG dbwipnpjmpjwG qbajpniii hiubwqwpd wpwqmpjmGn bmGbGw mqpq 
wpwqmpjwG niqqmpjniGp: O-pw hwiSwp v' hwpwpbpwbwG wpwqmpjniGp iSbGp ilfein bwGGwGGGp 
hwbwqwpd lupwqmpjmG b ?hGp oqmwqnpfrp hwbwqpp lupwqmpjmG wpmwhwjmmpjmGp, bpb tfi uiuGmii iSbb wji pmG: 
UjuwpuniJ GbGp iSp2in bwbGwpbbGp pwgwuwlpuG dbwipnpjmpjmGGbpp qnjmpjwG ppwGmGpp: 

Upqp Ippqplpujnui lihQp iSfyin oquiuiqnp&nuS hQp rpnulpuG dUuiipnJunLpjnLQQtipp U ijpiuQgpg uinuig qMuft lupnjnLGpGtipp, 
puiguinmpjuiiip npn2 nhiqphpp hpp iuQhpuidh2uinipjniQ t qqiugq'rmS qppuintu puiguiuuilpiiG dUunpnJunipjniQQhpp, pQ^iqhu 
oppQiuli iniupiufriulpuG hiujhpiijpQ uiGrunurpupdiSiuG nhiqpnui: 



Ujchi IpxnniupoGp Qnp Q2uiQuiljniiSQhp: £uiQp np, huniuiduijG (1.2 - 3)-p, (1.2 - 12)-p U (1.3 - 27)-p, pnpip / 2 (v), 
y' 2 (v'), Pi(v) U P^iy') qnp&iuqpgGDpp l}iuju0 1 ui& qG lipuijQ y,(v) U /j(v') qnpfriuqpg G hppg , pG^iqQu QiuU hiuiiuidujjQ 
(1.3 - 9)-p U (1.3 - 20)-p p\ U y\ 5>niQl}gpiuQtipp QmjQ /?i U y 5>niQl}gpiuQtipQ hQ, uiupu huiQmQ iquipqiiipjuiQ U 
qhrpuqpiniuquiQ huiiSnijpp, iShQp hhuiUjun qnp&iul}pg-4)niQqgpujQtipp lihg puig qpnqQhQp uuinppQ gmgp^Qhpp. 



Pd )=>J8( 

/i( ) => r( 



) 



1.3-37 



UjQmhhinU lippuinhpiq' dhp (1.3 - 9)^4 U (1.3 - 20)-ni[ uuiuigui& lupqjniQpQtipp (1.2 - 15)-p iSq$>, pQjiqhu QiuU oqinLjtil 111 ! 
(1.3 - 37)-ni[ inpi[iU(J iSbp Qnp Q2UiQuiqnnSQhppg, lihQp hiupiuphpuilpuQ 2iupdiiujQ mn]ir[ U huiquiquipd dUuiq^ntunLpjniQQtipp 
hunSiup quinujQuiQp hDmUjuiLhuiqMjiuuipnuSGhpp huiiiuil}iupqp. 



16-82 



Upui^uiip Injhpp <uipuiphpuilpiiG CuipdiiuiG ShumpjniG 



Hiqpq dhuiipnpinipjniGGhp 4,uitpnquip<i dhuiipnpinipjniQGhp 

f t> = P(v)t + gy(v)-^-x J t = P(y')t' + gY(y')^ r x' 

I *' = 7(y)(x-vt) x = y(y')(x' -v't') 



1.3-38 



\ji5uiuuiiqhu llppuinhmi[ iShp (1.3 - 9)-ni[ h (1.3 - 20)-rul uuiuiguifr uipqjniGpGhpp (1.2 - 16)-p dhj, pG^iqhu GuiL 
GmjGiqbu oqinqMimil (1.3 - 37)-niJ uipihii& lihp Qnp G2 UJ G UJ 4 nu 5G D Pl 1 9i iShGp huipuiphpuilpiiG 2uipdiSuiG niqpq U huilpiiquipd 
dumipnpinipjnililihpp huiiSuip IpiuiuiQuiGp Guih hhuihjuq huiipiiuuipnuilihpp huiiSuilpiipqp. 

fliqpq dhuiipnpinipjniGGhp 4,uilpiiquipd dhuiipnpinipjniGGhp 

*' = />(v)(t -*-£*) u f t = /}(v')(t' - g-^x'^j 1.3-39 

x' = y(y)(x- vt) I x = y(y'){x' - v't') 

<p2hgGhGp np iShGp qhn iqhuip t npn2hGp y8 h y qnp&wljpg-IJmiGljgpuiGhpp, pG^iqhu GuiU v' U v huipuiphpuilpiiG 
uipuiqnipjniGGhpp lipgU hqui& uinGyiipjniGp: 



1.4 - ^uiuuiuiuiniQ lIfiuiqnipjniGGb]i]i Q-niiSuijiiSuiQ U ^uiGiJuiG PuiQuidUhpii 

bGpuiqphGp uipihii& hG hphp K, K' U K" pGhpgpuq huiiiuilpiipqhpp, npuihq K' pGhpgpiiq huiiSuilpiipqp K pGhpgpuq 
hunSiuqujpqp QquiimSuuSp 2iupdi[niii t v hwuuiuiuiniG uipuiqnipjuiiip, pulj K" pGhpgpuq huiiiuilpiipqp K 1 pGhpgpuq 
huiiSuilpiipqp GlpjiuiiSuiu'p 2uipdipiiu' t u huiuuiuiuiniG uipuiqnipjuiiip U K pGhpgpuq huiiiuilpiipqp Glpiiuiiiuiiip 2uipdipiiu' t w 
huiuuiuiuiniG uipuiqnipjuiiip: 

CQqq&md 1 -9 - imiiSuijiulpuG uipuiqmpjwrfp jiupdi/nij ip.npdGuibiuG duiuGJibp wpwqnipjmGp (mju piudGmiS K" 
JiGbpgjiwi hiuiSwlpiipqli huiuuiuiuiniG wpwqmpjniGp) K' L K fiGbpgliwi huiGuibuipqbpfi GbuimiSuiiSp, unilnpwpwp 
G^uiGuibi/niG t huiGuiu/uiuiuiufuuiGuipuip u' h u uiuinuiG^uiGGbpnu': fiuijg GbGp qbpuiijuiubgfiGp npuiGg i/infuuipbG 
oqmwqnpdbi huiGuiujuiuiuiupjuiGuipuip u L w mwnbpp, [iub GmjG muinbpji ]uuiquiG2q'uid miunbpp q'bpuiuiuihbinq' uijij 
huiGuiujuimuiuJuuiG uipuiqnipjmGGbpJi hwhiuipupd wpwqmpjwG G^uiGuiljGuiG hwiSwp: 

f l-pimupqhQp K" pGhpgpuq huiiSuilpiipqp uljqpGuilpjinp 2uipdnuip, npp GmjGu[hu K' pGhpgpuq huiiSuilpiipqp GlpiiuiiSuiiSp 
2UipdUnui t u huiuuiuiuiniG uipuiqnipjuiiip h K pGhpgpuq huiiSuilpiipqp GlpuiniSuiiSp* w huiuinuiinniG uipuiqnipjuiiSp: 
lIjGnihhinL qpuiGghGp K" hGhpgpuiL huiiSuilpiipqp uljqpGiiiljhinp 2uipdniiSp duiiiujQuiqp hpbni uiuipphp upuhhpp huiiSuip: 
UlpqpGuiljhinp 2uapdiiuiQ duiiSuiGuilpiiinuipuifruijpG uinuiGgpuipilhpp inuipphpnipjniQp, uijq hpqm uiuipphp 
ujuihhpp-ujuiuiuihuipQhpp lipgh, K' h K pQhpgpuq hunSuiliuipqhpnuS IjniQhQuiQ hhuihjuq uipdhpQhpp. 

K ! pQhpgpuq huiiiuil}uipqniii K pQhpgpuq huiiiuil}uipqniii 

h-h=t 1-4-1 

X2 — X] — X = Wt 

Uhp hui2ilmii(ihpp l}uiuiuiphpii huiiiuip lihQp oquiijhpii hQp (1.4 - l)-ni[ uipi[ui& Q2UiQuil}niii(ihppg U (1.3 - 38)-nL[ uipi[ui& 
huipuiphpuil}uiQ 2uipdiiuiQ niqpq h huilpiiquipd dUuiipnhinipjuiQ huii[uiuuipniiiQhppg: 

♦ Oqim/hGp mppp dhmifrnJumpjuiG hwrfiumupmiSGhplig 
Q-phQp (1.3 - 38)-ni[ uipi[ui& mqpq dhuiipnpinipjuiQ huiihiiuuipnuSGhpp uijq hpl}m uiuipphp ujuiuiuihuipQhpp huiiSuip. 

P(v)t 2 + gy{v)^X2 f t\ = p(v) tl + g7 (v)^x l 

c U < c 1.4-2 





17-82 



4,iujlpulpiiQ -iuipiuphpiulpxiQnipjiuQ ^uiinnilj ShunipjmQ 



OquiU 1 hpiU 1 (1.4 - 2)-niJ inpU^uS iujij hplpu upuiniuhiupQhpp uiniuQgpiupilhpp ninjiq 6hiui|intunipjiuQ huiipiiuuipnuSGtippg, 
huyilhQp npiuQg lipgU diuuiuQiuljp inhnrpupjniQp h hhnuu[npnipjniQp hhinujun Iphpup 



p(v)(t 2 



t,) + gr(v)-^-( X2 



-*0 



1.4-3 



x' 2 -x\ = y(v)[(X2 -X\) -v{ti - ?i)] 



lIjQnihhinL (1.4 - 3)-p uh$> inhrpunphpu[ (1.4 - l)-ni[ inpipiifr hplpu upuiniuhiupQhpp inhnrpupjiuQ U hhnunpipnipjiuQ 
uipdhpQhpp, uhQp IpnniuQiuQp. 



t' = [p(v) + gr (v)^-]t 

ut' = y{v){w - v)t 



1.4-4 



f'piup i)puj piudiuQhpiil (1.4 - 4)-p hplipnpn U uiniujpQ hiuihiJuiupniuQhpp uhQp IpnniuQiuQp hiuuuiiuuiniQ 
uipiuqnipjniQQhpp hiuQiiiuQ piuQuidhp. 



y(v)(w-v) 



1.4-5 



♦ Oquii[bGp hmbwiiwpd dbwipnpjmpjwG huidwuwpmiSGbppg 
IphQp (1.3 - 38)-nil inpipii& huil}iurpup6 dhuupnpinipjiuQ huuliuuiupmuQhpp uijn QmjQ hplpu upuiniuhiupQhpp huuiiup. 

ti = P(y')t' 2 + gr(v') -4-4 [ f i = P(y')t\ + gr(v') -^-*i 

c- U < c 

x 2 = r(y')(x' 2 -v't' 2 ) I xi = r(v')(^i -v'f'j) 

Oquulhpul (1.4 - 6)-ni[ mpi[iu& iujij hplpu upuiniuhiupQhpp uiniuQgpiupilhpp hiulpuruupd dliiuipnJunipjiuQ 
huuliuuuipniuQhppg, huyilhQp npiuQg lipgh diuuiuQiul}p inluirpupjniQp h hhniuilnpnipjniGp hhinhjuiL Iphpu}. 

t 2 -h = P(v')(t' 2 -t\) + g Y (v')\(x' 2 -x[) 

c 

x 2 -xi = y(y')[(x 2 - x\) - v' (t' 2 - t\)] 

UjQnihhinh (1.4 - 7)-p uh$> inhrpunphpul (1.4 - l)-ni[ inpipiifr hplpu upuiniuhiupQhpp inhnrpupjiuQ U hhnuulnpnipjiuQ 
uipdhpQhpp, uhQp IpnniuQiuQp. 

t = [p(v')+ gY (v')^y 

wt = y{v'){u - v')t' 

f>piup i)piu piudiuQhpiil (1.4 - 8)-p hplpinpq U uiniujliQ huuliuuiupmuQhpp uhQp IminiuQiuQp hiuuuiiuinmQ 
uipiuqnipjniQQhpp qnuiiupuiuQ piuQiufihp. 



y{v')(u-v') 



bph uhQp hiupiuphpiulpuQ uipiuqnipjniQQhpp qnuiiupuiuQ U hiuQiiiuQ qnpdnrpupjniQQhpp Q2iuqphQp hhinhjuiL Ijhpiu. 



W = U iff V 

u — w Q v 



1.4-6 



1.4-7 



1.4-8 



1.4-9 



1.4-10 



llupu (1.4 - 5)-ni[ h (1.4 - 9)-ni[ inpipxifr huiumuunniQ uipiuqmpjmQQhpp tuuQuiuQ U qnuiiupuiuQ piuQui&hhpp qphpul 
uJuuufiQ h oqinuiqnpdhpul (1.4 - 10)-nil inpiliu& Q2iuqpniiSQhpp, uhQp IpnniuQiuQp. 



u - w Q v = 



y(v)(w- v) 

PW + gYiv)^ 
c 



W = U © V = 



y(v')(u-v') 



1.4-11 



18-82 



Upuj^uiip Q-njhpp <uipuiphpiuquiG CuipdiiuiG ShumpjniQ 



1.5 - kuiiSuijuiljuiQ U]iuiqnipjniQQh]i]i Q-niiSuipiSuiQ U ^uiQiJuiQ PuiQuidUhpii 



Ujdii tl hdpuiqphQp np ipnpdQuilpuQ duiuQplpi iSpui^iuip iniupiu&nipjiuQ ilhg 2uip<}ilniiS t IpuiJuijuiquiQ uipuiqmpjimSp U 
uijq ipnpdQiuljujQ iSuiuQplip uil}QpuippuijpQ uipuiqnipjniQQhpp K' U K pQhpgpuiL hiuiSiulpjjpqtipnuS iSUQp QnijQujbu 
qQ2UiQuit[hGp huiiiuiiquiinuiuJuuiQuipuip u U w iniunhpnil U ijpuiGg lih&nipjmQQhpp IpipryqMjQ hhinUjun qhpu}. 

&- = u 
dt 

df = w 
dt 

'l-p^JphphQghpiq' (1.3 - 38)-ni[ uipilui& huilpurpiipd dUunpnJunipjiuQ huiqMjjuiupiuiSGtipp puin t' dunJiuGuiqp U uijGuihq 

inhrpuiiptipiil f -=2j- J-p uipdhpp (1.5 - l)-pg, iShGp IpnnuiGujGp. 



1.5-1 



dt 
dt' 

dx 
dt' 



«v') + *r(v')-*f 

c 
y(y')(u-v') 



1.5-2 



(1.5 - 2)-p hplipnpij hiui[iuuiupniiip piudiuGhpiil uinuigpQ hiuipxiuuipiiuiG djiui iShGp IjuinuiGuiQp uijq ipnpdQuilpuQ 
iSiuuQpqp iul}QpuippuijpQ uipuiqmpjiuGp K pGhpgpuiL himSuiquipqp Q quiunSuuSp , iupuiuihuijuii[iu& v' U u 
uipuiqnipjmQQhpni[, npQ X.\ hhQg hiuGijpuuiGnuS t hplpu u U v lupiuqnipjniGGhpp qnuSiupiiiuG piuQuidUp. 



dx 
dt 



r(v')(«- v') 
P(y') + gr(y') 



1.5-3 



V II 

,.2 



XiihuGuiiqhu qp^hphGghpiil (1.3 - 38)-ni[ inpipufr mripq dloudintunipjuiG hiui[iuuiupniiiQtipp puin t dunJuiQuiqp U 
uijGuihq uihrpuqphpiq' I ^j- J-p uipdhpp (1.5 - l)-pg, iSbQp IjuinuiQujQp. 

dt' 



— = i 3(v) + gr (v)^ 



1.5-4 



dx' 
dt 



r(v)(w-v) 



(1.5 - 4)-p hpljpnpri. hiui[iuuuipniiip piudiuQhpiil umuigpG himpiiuuipiiuiG djiui iSUGp IpiinuiGuiQp QmjQ ipnpdQuilpuQ 
uuiuQpqp uiljQpuippuijpQ ujpuiqiupjiuGp K' pGtipgpuiL huiuuilpxipqp Glpuiniiuiup, uipinuihuijinU 1 ui& v U w 
uipuiqmpjiuGQGpnil, npQ t^ hhQg huiQnpuuiGnuS t hplpu w U v ujpuiqnipjniQQhpp huiQiiuiQ piuGuidLp. 



dt' 



y(v)(w-v) 
vw 

,.2 



j3(v) + £y(v) 



1.5-5 



(1.5 - 3)-ni[ U (1.5 - 5)-ni[ inpipufr hplpu uipuiqiupjiuQQhpp huiQuuiQ U qiuiiuipuuiQ puiQuidhhpp qphpiq 1 lipuiupQ U 
oqinuiqnpdhpiq' (1.4 - lOJ-nq 1 uipdjUift G2UiqpiuuGhpp, lihGp quuuuGuiQp. 



u — w Q v = 



7(v)(w-v) 
c 



W = U © V = 



/(v'JtM-V 1 ) 

0(v') + sr(v')^ 



1.5-6 



CQqq&nnI 1-10 - UbGp wbuGmd hGp np (1.5 - 6)-ni/ mpdiud IjiuifwjuiljujG wpiuqnipjmGGbpfi hmMiuG h qmiSuipdwG 
pwGwdlihpn d2qppin l/bpu/nd hujrfpGl/Gmrf bG (1.4 - ll)-nd inpdwd hwumwmmG wpwqmpjmGGbpp hwGdiuG h qmilwpdiuG 
pmGwdbbpp hbui: ■(hwhwpiup wpwqmpjmGGbpp hwGilwG b qmdwpdwG pwGwdbbpp Gwfudwfr jbG wjG pwGpg pb wjn 
wpwqmpjmGGbpp hwumwmmG bG pb ijpwGp mGbG bwdwjwbwG whGpwppwjpG pGmjp: UjGwbu np wjn pwGwdbbpp tfp/w 
bG b pGbpgpwi hwdwbwpqbpp ppwp Gbwwdwdp mGbgwd hwpwpbpwhwG wpwqmpjmGGbpp hwdwp, b ipnpdGwbwG 
dwuGpup bwdwjwbwG ^wpddwG wpwqmpjmGGbpp hwdwp: 



19-82 



4,uijlpxilpiiQ <uipiuphpuil}iuQnipjuiQ ^imnniAj ShunipjmQ 



(1.5 - 6)-p lihg luniujpQ huiqMjiuuipiuup pufrhpiq' puin w uipuiqmpjuiQ U hpljpnpri. himhuuuipnLiip pii&hpii[ puui u 
uipuiqmpjuiQ, iShQp uiqQpuippuijpQ lupiuqnipjiuQQtipp qnuSuipiiuiG U hiuQiSuiQ huiiiuip IpiiniuQiuGp QuiU hhuiUjunpiuQuidlihpp. 



w = u kB V 



U = W fcj V 



P(v)u + y(v)v 

r(v)(i-*-p-) 

P(v')w + y(v')v' 
7(v')(l-g^f) 



1.5-7 



Ujchi lipiuupQ qphQp (1.5 - 2)-p L (1.5 - 4)-p iSpiujG umuigpG himhuuuipnuiGtipp. 



dt 
dt' 

dt' 
dt 



P(v') + gf(v')- 



= P(y) + gy(y)- 



1.5-8 



llj QnihhuiU (1.5 - 8)-p uinuigpG himhiiuuipiiuiG iSh$> qppuinhpii[ (1.3 - 26)-p U hpqpnpq huiq'uiuuipiSuiQ lihg IjppuinQpiq' 
(1.2-9)-p, lihQp UuuiuiQuiGp GuiL htunLjuiL puiGiudLhpp. 



dt' 

dt' 
dt 



P(v')(l-g^) 



1.5-9 



= j8(v) 



f*piup hhin puiqiSiuunuuiUhpiiJ (1.5 - 8)-ni[ inpipufr himhuuuipnuiGtipp hiuiSiuUuipqp uinuigpQ U hpqpnpq 
himhiiuuipnuiGtipp, iSUGp IpnnuiGuiGp hhinUjuiL uinGyupjniGp. 



[i?(v') + gr(v , )^r][i3(v) + gr(v)^ L ] 



l 



\>i5uiGuiiuhu ppuip hbm piuqiiuiupuinlphpiq' (1.5 - 9)-ml uipU_uj& huiqMjjuuipmu'Gtipp huiiiujlpiipqp uiniujpG U hpljpnpn 
hiui[iuuiupniii(ihpp, iSUGp IpnnuiGuiQp QuiU hhuiUjun uinGyupjiuGp. 



/3(v)/5(v')(w-p-)(l-^) 



= 1 



1 4.hphp2tipiq' (1.3 -23)-p, iShGp (1.5 - ll)-pg IpnnuiGuiGp htunLjuiL umGyupjniGp. 



P(v)P(v') = r(v)r(v') = 



i 



0-^)0-^) 



> 



1.5-10 



1.5-11 



1.5-12 



t>piup hhin himStuSimntipiq' (1.3 - 34)-nq' U (1.5 - 12)-n4 uip4ui& lunQyupjiuGGhpp iShQp IpnnuiQuiGp hhinLjiUL qhnhgpli 
uinGyupjniGp, npp ppiup hhin t quiiqmii hplpu iniupphp pGhpgpuiL huiiiuilpupqtipp Qlpuiniiuiiip IpuiSiujuilpxiG 2uipd4 nr l 
ipnpdGiulpiiG liuiuGpljp u U w uipuiqiupjiuGGUpp U GmjG pGhpgpuiL himSiuUuipqtipp ppuip Ql}iuiniiuiiipniQhgui& v U v' 
mnjiri U hiuquiqpp huipiuphpuiUuiG uipiuqnLpjiuGQhpp hhui: 



0-^)0-^) 



1 



1.5-13 



CGiiq&nuI 1 -1 1 - bpb dbGp nGqniGbGp np ipnpdGwl]wG iSmuGpl]p K' pGbpgpwi hwiSiubwpqp GlpumiSwiSp qinGi[miS t 
wG^iupd UptiwhmiS, wjupGpG u = 0, uiujui pGwlpuGwpmp wjG K pGbpgpwi hwdwbwpqp Gl/wwdwiip 2iupddmG t W = v 
huiuinwinniG wpwqmpjwdp b hbuiLwpwp (1.5 - 12) -nd mpdiud pwGwdhn qwnGmiS t (1.3 — 34) -nd inpdiud pwGwdhn, pub 
(1.5- 13) -nil wpi/wfr pwGwdbn niunGmtS t GmjGmpjmG: 



20-82 



Upuj^uiq'i Injupp ^uquupupuiquiG CuipdiiuiQ ShumpjniQ 



1.6 - ^uignjiri.uiliuiQ 9Uuii|intunipjniQQh]i]i kfi]iuinnii5ii 

£uiQp np, huniuiduijG (pQqq&miS 1-2)-p, huquuphpiulnuGnLpjuiQ hujuimq uihunipjuiG iSq$> ppiup Glpxnniiunip 
hiupiuphpujl}iuQ 2uipdiiuiG iSq$> qinGU_nq fiGhpgpuq huuSuiqiupqapp uiniuQgpuipilhpp duunjinpinipjuiG hiui[iuuiupniiiQhpp puin 
duuSuiQuiljp U uiuipui&mpjuiG ujauip t iJiQhQ qfriujpG hQ, hhuiUiupiup qpuiQp iqhing t puiiJuipuiphQ qduijpG dLuiipntunipjuiG 
pnpip hpiSGuilpuG ophQpQhppQ: 4uniuiduijG qdiujpG dLuupntumpjuiG uiiihGuihpiSGuiliuiG opuQpp huipuipapujlpiiQ 2 UJnc W m Q 
hiusmpquilpxiQ q&uijpG dUunpnJunipjniGGhpp umiujujgQnuS hG iSp Gnp QiSuiGunnpiq q&uijpG dliUiipnpmLpjmQ: 

flpujQuqp dhGp uiupugnighGp np (1.3 - 38)-niJ uipipuft huipiuphpuiquiG 2uipdiSuiQ dUunpnJunipjuiG huupuuujpniiSuQpp 
puidjupiupmiS hG qdiujpG dUuiGin[unipjniGGhpp uidhGiuhpiSGuiquiG ophGppG, uiupii qpui huuSuip quiimuphQp hiusmpqiulpiiQ 
dliiuGintunipjniGGhp U upuhuiGjhGp np uuiuigipiifr uipqjmGuipuip dUuiGintunipjniGp Gmjuiquu l]iQp Qmj Guunfiu] 
dLuupnpmipjniQ, uijupGpG ujjQ niQhGui GnijG inhupp: llju fiuiGuuuuiphml iSuGp l}l}iupnquiQuiQp npn2tq iSQiugiud uiQhuijui 
qnpduiqpgGapp uipinuihiujinnipjniQQhpp quid uijq qnp&uiqpg Qhpp iSpgli qnjmpjniG mGugnq uinGyupjniGGapp: 

bGpmqpuGp np uqupxifr hG hpap K, K' u K" JiGhpgpuq huuSiulnupqapp, npinuq, huiiiuiduijQ (pGqqdmiS 1-9)-p, K' 
pGupgpuq huniuilpxipqp K pQhpgpuq huiiSuiquipqp GquiunSuuSp 2iupdO l mii t v huiuuiuiuiniQ uipuiqmpjuiiip, puq K" 
pGupgpuq huiiiuiljuipqp K 1 pGupgpuq hiuiiujl}uipqp Ql}unniiujiip 2uqidipuiS t u huiuinuunmG uipuaqnipjunSp u K pGhpgpuq 
hunSuiqiupqp QqiuunSunSp 2uipdd l nui t W huiuuiuiuiniQ uipuaqnipjunSp: 

Ujdii oquiq'hpiil (1.3 - 38)-niJ uipipuft huqnupupuiqujG 2uipdiSuiG dUuiqhnJunipjuiQ huupuuujpnuSGuppg, qphGp q ,a P nn t2J ua L 
hphp pGupgpuq huniuilpiipqupp mqpq U luulpiiquipd dUuiqhnJunipjuiQ huupuuuqiniiSGupp iSpiSjuiGg QquiuuSuuS huinujuq qtqnq. 



♦ PLwipnfunipjLuG hmiliuuiupnidGhpp K' L K pGhpgpwi hwiSiubwpqhpp iSppb 

Hiqpq dUuiq^inJunipjniQQhp 4,uiquiquipd dliUiq^nJunipjniQQhp 






y(v)(x-vt) 



t= P(v')t' + gy(v')\x' 
c 

x = y(y')(x' - v't') 



1.6-1 



♦ OhmipnpjnipjwG hwilwuwpmiSGhpp K" b K' pGhpgpwi hwUwhwpqhpp itpph 

Htqpq dliUiqhnJunipjniQQhp ^uilpuqujpd dUuiipnpinipjniQQhp 

/ = P(u)t' + gy(u)-^-x' | t' = P(u')t" +gy{u')\x" 



y(u)(x' - ut') 



x' = y{u')(x" — u't") 



1.6-2 



♦ £>kwipnpjmpjiuG hwilwuwpmiSGhpp K" L K pGbpgfiwi hiuiSiulpiipqbpp iSpgL 

fUqpq dUuiq^nJunipjniQQhp <uiljuiquipd dUuiq^nJumpjniQQhp 



t" = p{w)t + gy{w)\x 



x" — y{w)(x — wt) 



t= P(w')t"+gy(w')\x" 
c 

x = y(w')(x" - w't") 



1.6-3 



flpuihq K, K 1 U K" pQhpgpuq hunSuiqujpqhpp v', u' U w' huiljuiquipd huipuaphpuiquiQ uipuaqnipjniQQhpp 
uipuiuihuijuinipjnLQQhpp, huiiiuidujjQ (1.2 - 8)-Ji U (1.3 - 37)-p Qnp G2UiGuiqnuSGQpp, qiJiGhG. 

v = - v U u — - u U W = -~hr — w 

p(v) P(u) p(w) 

t>ul} (1.3 - 32)-n4 uipq^uicJ pujGuidUhpp l}ppuinhpiil K, K' U K" pQhpgpuq hujiiujl}uipqtipp niqpq U hujl}uiquipd 
uipuiqnipjmQQhpp hunJujp, pQ^ujhu QuiU GmjQiqhu q^bph^hpiq^ (1.3 - 37)-p Qnp Q2iuQiulpiuiQapp, iSbQp l}uuiuiQuaQp hhuiUjuj^ 
puiQuidlibpp. 



1.6-4 



21 -82 



4,uijl}iuliuiQ -iuipiuphpuilpuQnipjuiQ ^imnniAj ShuiupjniQ 



/J(v') = 
y(v') = 



7(v) 
d(v) 

goo 

«f(v) 



««') = 



r(V) = 



rO) 

d(u) 
d{u) 



p(w') = 
y(w') = 



d{w) 

P(w) 
d(w) 



1.6-5 



Ujdii oquiqMjpiq' (1.6 - l)-nq\ (1.6 - 2)-ni[ U (1.6 - 3)-ni[ inpiluifr nlr lpil ^ hiulpuquipd dUiuipnpimpjuiQ 
himliuuuipnuiQtippg, IpuimuphQp duiiSuiQuiljp U uiuipui&nipjuiG hplpu huignpquilpuG dUuiipnpinipjniQQhpp prqnp hGuipiuipip 
i[hg iniupphpiuqQhpp: Ujq prqnp hiusmpquilpuQ dUunpnJumpjniQQtipp quiuiuiptqmg hhuin iShQp IpnniuQuiGp v, u U w niqpq 
ujpuiqmpjniQQhp U ijpuiQg huil}iurpup6 v', «' U w lupiuqnipjniQQtip opupniQuilinq qnp&iul}pgQhpp lipjU hquj& pnpip 
uinGyupjniGGtipp: 



1. OqtndbGp (1.6 - \-)-ni[ mpi[w& diudiuGwl/fi U inwpiudmpjwG mqfiq dhim[mpjnipjwG hwilwmiipmdGhpIig 



^pui huiiiuip (1.6 - 3)^4 uip^iuft huilpurpupd dUunpnJunipjuiQ huiqMjjuuipnuSGhppg f-p U x-p uipiniuhiujinnLpjiuGQhpp 
inhrpuqptqni[ (1.6 - l)-ni[ inpipufr duiiSuiQuiljp U uiuipui&nipjuiG mqpq dlauLpnpiiupjuiG himliuuiupnuiGtipp iSh$>, dhQp 
quuiuiQuiQp. 

t' = [p( v )p( w <) - gr (v)y(w')^y' + gy(w')[p(v)^ + y(v)-^y 

x = y(v)y(w')f[ - g^-\" - y(y)[r(w')w' + P(w')v]t" 

(1.6 - 6)-ni[ inpipufr dUuiLpnpinipjniQQhpp uipiniuhiujimupjiuGGhpp huiiStuSimnhpiq' (1.6 - 2)-nU 1 inpU^uS t' duiiiuiGuilip U 
x' uiuipui&mpjuiQ hiulpuquipd dUuiq^inpinipjuiQ hiuipuuiupnuiGtipp hhin U ppuip huiqMjJuuipagGtqnil f"-p U x"-p 
qnp&iuqpgQhpp, iSaGp IpiinuiGuiGp htnnLjuq umGyupjniQQhpp. 



1.6-6 



chjjiiuiGuilip duuidinpinipjniGpg 

P(u') = P(v)p(w')-gy(v)y(w')^f 

c 

y(u')u' = y(w')[P(v)w ! + y(v)v] 



Suipui&nipjuiG dLuidinpinipjnLGpg 

r(«') = r(v)r(w , )(i-g J ^) 

y(u)u = y(v)[y(w')w' + P(w')v] 



1.6-7 



2. OqtndbGp (1.6- l)-ni[ mpdwd dwtfwGiub[i b wwpw&mpjiuG hwbwpwpd dbmdmpjnipjwG huiduiuuipnidGbpfig 



'l-pui huiiiuip (1.6 - 2)-nU [ inpU^uS hiulpuquipd dUuiipnpinipjuiG huiqMjjuuipnuSGhppg f'-p U x'-p uipinuihuijimupjinGGtipp 
inaquiqptqnil (1.6 - l)-ni[ inpipufr duiiSuiQuiljp U uiuipui&nipjuiG hiulpuquipd dlouUinpinLpjuiG huiipuuuipnuiGapp iSh$>, lihGp 
IpiinuiGuiGp. 

t = [/J(v W) - gr(v')r("')^ }" + g-^Y(.u')[P(v')u' + y(v')v']x" 

x = r(v')r(«')(i - £^)*" - r(v')[r(«')«' + J8(»>']«" 

(1.6 - 8)-ni[ inpipufr dLuiipnpinipjniGGapp uipinuihuijiniupjiuGGhpp huuStuSuiinhpiq' (1.6 - 3)^4 uipdjiuft t duiiSuiQuiljp U 
x inuipui&nipjuiQ Inuljuiquipd dUunpnJunipjuiQ huiq'uiuuipmiSQhpp hhui U ppuip huii[iuuiuphg Qhpiq 1 f"-p U x"-p 
qnp&iuqpgQhpp, iSUGp l}uinui(iujQp hhinUjiu^ uinQjnipjniQQhpp. 



1.6-8 



cfujiiujQuiqp dLujq'inpmipjniQpg 

p(w') = p(y')P(u')- gy(v')y(u')^f- 

c 

y(w')w' = y(u')[fi(y')u' + y(y')v'] 



SuipiudnipjiuQ dUunpnJunipjniQpg 

r(w , ) = r(v , )/(«')(i-g^f ) 

y(w')w' = y(v')[y(u')u' + P(u')v'] 



1.6-9 



22-82 



Upiu^iuip Injhpp ^lupiuphpiulpiiQ CiupdiiiuQ ShumpjmQ 



3. Oqmq'hGp (1.6 - 2)-ni[ mpi[wd dujifiuGwl/p L inwpwdmpjiuG mqpq dhwipnpjmpjiuG hwilwmiiprmSGhppg 



'l-piu hiuiiujp (1.6 - l)-ni[ uipihjj& nujpq dluuipntunipjiuQ hiuiliuuiupniiSQappg ?'-p U x'-p uipiniuhiujinnipjniQQQpp 
inQrpun,pQpiil (1.6 - 2)-ni[ inpinufr dunSiuQujl}p U uiiupiu&nipjiuQ ninjnj dhuuhnpimpjiuQ hiuiliuuiupnuiQupp iSq$>, lihQp 
IpjuiiuQuiQp. 



t" = [«v)/j(«)-«r(v)r(«)^-]« + *-^-r(v)[r(«)« + ««)v>c 
x" = r(v)y(«)(i - s-jg-)* - r(«)[P(v)« + r(v)v]t 



1.6-10 



(1.6 - 10)-ni[ inpipufr dUuiipnpanipjniQQhpp uipiniuhiujinnipjniQQhpp hiuiSQiSiuinhpiil (1.6 - 3)-nil uipiliuft t" dunJiuQiuljp 
U x" uiiupiu&nipjiuQ ninjnj duiuinnpinipjiuQ hiuiliuuiupnuiQupp htun U hpiup hiuiluiuiupagQapiil f-p U x-p qnp&iuljpgQtipp, 
iShQp IpiinuiQiuQp hhinUjuiL lunQyiipjniQQtipp. 



chuiiuiGuilip dUiuLpnpanipjniQpg 

PM = P(v)P(u)-gr(v)r(u)^f 

c 

y(w)w = y(v)[y(u)u + ff(u)v~\ 



Siupiu&mpjiuQ dUuiipntumpjniQpg 

y(w) = r(v)r(«)(i-*^-) 

y(w)w = 7(m)[/J(v)m + y(v)v] 



1.6-11 



4. OquidhGp (1.6 - 2)-ni[ wpi/iud diuifiuGwUp U inwpiudmpjiuG hwuwqiupd dhwipnpjmpjiuG hwiJwuwpmGGhppg 



^piu huuiiup (1.6 - 3)-ni[ uipi[iu& mqpq dUiuipnJunipjiuQ hiuihuuiupniu'Qtippg f"-p U x"-p uipiniuhiujinnipjniQQhpp 
inDrpunjiapiil (1.6 - 2)-ni[ inpinufr dunSiuQujl}p U uiiupiu&nipjiuQ hiulpuniupd dhuuhntumpjiuQ hiuiniiuiupnuSQapp iSa$>, lihQp 
IpiuiiuQuiQp. 

t> = [p(u')P(w)-gy(u ! )y(w)^y + gj T y(w)[P(u , )w + y(u')u'}x 

x' = y(u')y(w)(\ - g^y ~ 7(u')[y(w)w + 0(w)u']t 

(1.6 - 12)-ni[ inpinufr dLiuihnhvinipjniQQapp UipiniuhuijinnipjniQQhpp hiuiStnSiuinhpiil (1.6 - l)-ni[ uipiliuft t' dunJujQuiljp U 
X 1 uiiupiu&nipjiuQ ninjnj dUiuihnpanipjiuQ hiuihuuiupnuSQapp hhui U ppiup hiuiniiuiupagQapiil f-Ji U x-Ji qnpfriuljpgQapp, iShQp 
IjuuiiuQuiQp hhuiUjun lunQyiipjmQQopp. 



1.6-12 



chuiSiuQiuljp dliunpnJunipjniQJig 

P( V ) = P(u')p(w)- gy(u')y(w)Mlf- 

c 

y(v)v = y{w)\_p{u)w + y(u')u'] 



Siupiu&mpjiuQ dUiuihnJunipjniQpg 

Kv) = r("')r(>f)(i-g-^f) 

y(v)v = y(w')[y(w)w + y8(w)u'] 



1.6-13 



5. Oqim/hGp (1.6 - T>)-ni[ mpijwd dwiSwGwhp h inwpw&mpjwG mqpq dhwipnpjmpjwG hwiJwuwpmGGhppg 



'l-piu huuiiup (1.6 - l)-nil uipiliuft huil]uin.uind dUiuipnJunipjiuQ hiuihiiuiupniu'QQppg £-p U x-Ji uipiniuhiujinnipjniQQhpp 
inQrpuijpapiil (1.6 - 3)-ni[ inpinnfr diuiSiuQuiljp U uiiupiu&nipjiuQ ninjnj dUuuhnpjnipjiuQ hiuihuuiupnuiQapp iSq$>, QhQp 
IpjuiiuQuiQp. 

t" = \_li{v , )p{w)-gy{v')y{w)^y + gj J y{v')[y{w)w + p{w)v']x' 
x" = y{v')y{w){\ - g^y - y{w)[p{v')w + /(v>']f' 



1.6-14 



23-82 



4,uijlpuquiQ -iuipiuphpuilpuQnipjuiG ^imnniAj ShuiupjiuQ 



(1.6 - 14)-ni[ inpipufr dUuiipnpinipjniQQhpp uipiniuhuijinnipjniQQhpp himStuSimnhpiil (1.6 - 2)-nU 1 mpiluift t" duiiSiuQuilip 
U x" uiuipuj&nipjujG luqpq dUiuipntumpjuiQ hiui[iuuiupniii(itipp htun U ppuip InuqMjJuuipagQtqnil f'-p u x'-p qnp&uil}pgQhpp, 
i5hQp IpainuiQuiQp hhinlijuiL umGyupjmQQapp. 



chjjiiuiGuiqp dUuiipnpanipjmQpg 

p(u) = P(v')p(w)-gy(v') 7 (w)^ 



y(u)u = y(v')[y(w)w + P(w)v'] 



SuipuidiupjuiQ dliUnpnJunipjniQpg 

r(«) = r(v'Mw)(i-g^f) 

y(u)u = y(w)[P(v')w + y(v')v'] 



1.6-15 



6. OqmdhGp (1.6 - 3)-nG mpi[w& dwtlwGwlip U inwpiudnipjwG hwbwpiupd dhwipnpjmpjiuG hwilwuwpmiSGhppg 



1-pui huiiiuip (1.6 - 2)-ni[ uipi[uj& mqpq duuiipnpiiupjuiQ hunluiuuipnuSGhppg f"-p u x"-p uipinuihuijinnLpjmGGtipp 
inhnuiqpapii[ (1.6 - 3)-ni[ inpipiifr duiiSuiQuiljp U uiuipui&mpjuiG huilpuqiupd dUuiipnpanipjuiQ himpuuuipnuiGtipp iShj, lihQp 
quuiuiQuiQp. 

r r > 1 

t = [P(u)P(w') - gy(u)y(w') H&- J*' + g±-y(u)[ 7 (w')w' + p(w')u]x' 



< 



r(u)r(w')(i - g^y - y(w')[p(u)w' + y(u) u y 



(1.6 - 16)-ni[ inpipufr dUuiipnJunipjuiQ uipinuihuijinnipjiuGGtipp huiiStuSuiinhpiq' (1.6 - l)-nij uipijuj& t duiiSuiQuiljp U x 
inuipuifrmpjuiG huilpurpupd dUunpnJunipjiuQ huiqMjjuuipmu'Qtipp haul U ppuip huuluiuuiptig Qhpiil f'-p u x'-p qnp&uiljpgQhpp, 
\5hQp IpiuiuiQuiQp hhinlijiu^ uinQyupjiuQQapp. 



cJ-uiiiuiGuiUJi duuiipnpimpjniQpg 

p(v') = p(u)p(w')-gy(u)y(w')^f 

c 

y(v')v' = y(u)[y(w')w' + P(w ! )u] 



Suipui&mpjuiG duuiipnpinipjmlipg 

r(v') = r(«)r(w , )(i-g^f) 

y(y')v' = y(w')[P(u)w' + y(u)u] 



1.6-16 



1.6-17 



Ujuu[puni[ iSuQp, hphp pGupgpuq huiiiuilpupqupp lipgU quiuiuiptiniil prqnp hGuipuiipip huijnpquilpuli duuiipnpinipjniGGapp 
uuiuiguiGp 24 huiui uinGyiipjiuGGtip: OqinqMjniil uijq huiipuuuipnuSGQppg, huignpq puidGnu5, lihGp qUuiuiuiphGp IpupUnp 
hhinUnipjniQQhp: 



1.7 - kuipUnp ^huiUnipjniQQh]i ^uignpri.uiljuiQ 9Uuii|infunipjniQQh]i]i kfipuinniiSfig 



Ujdii (1.6 - 9)-p duuSuiGuiljp duuiipnpinipjniGpg uuiuigiluifr hplpu huiipuuuipnuSGapp lihg uihquiqphpiq' (1.6 - 4)-nil 
inpipiifr piuiquupip ujpuiqnipjniQQhpp U (1.6 - 5)-nil uipipu& piuiquupip uipuiqmpjniG upupmQuilpiq qnp&uiljpgGhpp 
uipinuihuijinnipjinGGapp, pQjiqhu Quilt quiuiuipapiil npn2 lipfiimnnuiGhp, iShQp IpiinuiQuiGp htunUjuiL hplpu uinQyupjmQQhpp. 

rW = ^Sfrr(v)r(")('i-5 J f 

d(v)d(u) V c 1 



y(w)w — 



d(w) 
d(v)d(u) 



y(v)[y(u)u + P(u)v] 



(1.7 - l)-p luniujpQ huiiluiuuiprmSp hunShiSuiinhpiq' (1.6 - ll)-p iniupiu&nipjiuQ dliUnpnJunipjniQpg uuiuigi[iu& uiniugpQ 
himpuuiupiiuiG hhin quid (1.7 - l)-p hpqpnpq huiOjUiuiuprmSp hunSbiSiuintipiq' (1.6 - ll)-p dunSuiQujl}p dliUnpnJunipjniQpg 
uuiuigq , ui& hpqpnpq huidjUiuiupiSuiQ hhui, dUiuq^npampjuiQ npn2p^Qhpp huiiiuip lihQp quimuQuiQp hhuiUjuq uinQ^nipjniQp. 



d(w) = d(v)d(u) 



1.7-1 



1.7-2 



24-82 



Upui^uiip Injhpp 4uipuiphpuilniiG CuipchiuiG ShumpjniG 



Ujtfii ppuip huiihiiuuiphgGhpiq' (1.6-7)-nil, (1.6-9)-nil, (1.6- ll)-ni[, (1.6- 13)-nil, (1.6- 15)-nilU (1.6- 17)-nil 
inpipiifr huiipiiuuipnuiGhpp huiiSuilniipqhpp hpljpnpq huiqMiiuuipniu'Ghpp ui$> IpirpSp uipuiuihuijuinipjniGGhpp U Ipiiinuiphpiq' 
iSpliQmjQ uipuiqnipjniGp u uijq uipuiqnipjniQp upiipniQuilpiq qnp&uiljpgGhpp piupuiipipnui, iShGp IpiinuiGiuGp hhinhjuiL i[ a 9 
uinGyiipjniGGhpp. 



1) 

2) 
3) 
4) 
5) 
6) 



P(v)-r(v) _ p(w')- 7 (w') 



y(v)v 

)8(v')-r(v') . 

y(v')v' 
P(y)-7(y) _ 

7(v)v 

P(u')-y(u') 
y(u')u' 

P(y')-r(y') . 

/(v')v' 

/?(w')-r(w') 



y(w')w' 

_ P(u')-Y(u') 

y{u')u 

P(u)-y(u) 
y(u)u 

= P(w) - rW 
y(w)w 

= ft(w) - y(w) 
y(w)w 

P(u)-y(u) 



1.7-3 



iShj. 



7(w')w' y(u)u 

f>ulj oqinilbpiq' (1.6 - 4)-ni[ U (1.6 - 5)-ni[ inpipufr puiQuidLtippg, hQ2in t huiiinqilhl Iiduiujuil uinGyiipjniGGQpp 62 ulnl PJ ul G 

P(v ! )-y(v') _ P(v)-y(v) 



y(v')v' 

P(u')-y(u') 
y(u )u 

P(w')-y(w') 
y(w')w' 



y{v)v 

P(u)-y(u) 
y{u)u 

P(w) - y(w) 
y(w)w 



1.7-4 



Uj QiuhhinL (1.7 - 4)-niJ uipinii& uinGyiipjniGGQpp qppuinhpii[ (1.7 - 3)-p lihg, iSUGp IpiinuiGiuGp iSpiujG iShq uinGyiipjniG, 
npp lpupiihii& ^t ninjiq IpiiiS huilpuniupd uipuiqnipjniQQappg: UjupGpG uijq uinGyiipjniGp iSGnui t QnijGp IpiniuijuilniiG 
(v, M, wj niqjiq wpwqnipjniGGhpp u ijpmGg huilpiinuipd (y 1 , u 1 , wj uipuiqnipjniGGQpp huiiiuip: 4,tunuuipuip uijq 
uinGynpjniGp iqhinp t ihQp huiuinuiinniG iSQfrmpjniG, npp u iSGGp Ip^uiGuiUJiGp 4,2 inuinu^uiGnq' Iiduiujuil U.opuj. 

PM - r(v) = /?(«)-/(«) = PM - rW = P(y')-r(y') = /?(«')-/(«') = PW-rfr') =< = huiummuiniQ 

y(y)v y(u)u y{w)w y(v')v' y(u)u y(w')w' 2 

■fiuiGp np (1.7 - 5)-ni[ inpipiifr uinGyiipjniGp IpiiiSuijuilpiiG uipuiqnipjuiQ huiiSuip huiGnjiuuiGnuS t huiuuiuiuiniG lih&nipjniG 
u uijG, pGjiqtiu hpUnn5 t umGjnLpjmGpg, mGp uipuiqnipjuiG huilpiinuipd ^uiipnijuilpiiGnipjniQ, htunuuipuip lihGp uijq Gnp 4,2 
huiuuiuiuiniG lih&nipjniGp huipiuphphpiq' uiJiQqQpuilpiiG c uipuiqnipjuiG htun, IjqpDGp uijG htunhjuiL qhpu}. 



1.7-5 



<2 = S 



,J_ 



1.7-6 



flpinhij i-p duiiSuiGuilpiiinuipuidnipjuiG Qpljpui^uiipuilniiG IpiinnigqMii&pp pGnipuiqpnij tip Gnp huiuuiuiuiniG liu&nipjmG t 
U uijG pnpip pGhpgpun huiGuil}uipqhpniG mGp lipLGmjG uipdupp: 4,Duiuuipuip (1.7 - 5)-p qphpii[ iSpiujG ninjm U iSfiuijO 
huiljuiquipd uipuiqnipjniGGhpp huiiiuip, iSUGp l}uuiuiGuiQp hhuiUjun uinGjnipjniGGtipp hunSuilpiipqp. 



J8(v)-y(v) _ P(u)-y(u) _ P(w)-y(w) 



1 



y(v)v 

PW)-7(y') 

/(v')v' 



y(u)u 

P(u')-y(u') 

y(u')u' 



y(w)w 

P(w')-y(w') 

y(w')w' 



1.7-7 



,_L 



Lm&hpii[ (1.7 - 7)-ni[ uipi[ui& uinuigpG huii[uiuuipniGGtipp /J qnp&uiljpg Ghpp GljuiunSuuSp iSUGp IjuuiuiGuiGp hhuiUjun 
qhrihglil} puiGuidUhpp, npnGp fifyui hG liunSuijuiliuiG niqjiq uipuiqnipjniGGhpp hunSuip. 



25-82 



^.uijlpuquiG -iuipiuphpuilpuGmpjuiQ ^imnniAj ShuiupjiuQ 





r P(v) = r(y)(i + sf) 


< 


p(u) = r (u)(\ + s f) 




P(w) = y(w)(l+sf) 



1.7-8 



X>niQu}hu ^m&h^ni[ (1-7 - 7)-ni[ inpi^ 111 ^ tplipnpq hui4uiuujpnnSQtipp /3 qnp&uiljpgGtipp Glpuiniiuiiip, (1.7-8)-pQ 
hunSiuQiSuiQ, iSUGp IpiinuiGuiGp hhinUjuiL puiQiudUhpp IpuiSiujujlpiiQ huilpurpupd lupiuqnipjniQQhpp hiuiSiup. 



/J(v') = y(v')(l +*-£-) 

0(«') = r("')(i + 4) 

i3(w') = r(w , )(l+.s^) 



1.7-9 



P qnpdiuqpg (I hpp uipiniuhiujinrupjiuGGtipp (1.7 - 8)-pg inhrpuiyitipiil (1.6 - 4)-ni[ inpipufr hiulpurpupd uipuiqiupjiuGGUpp 
puiQuidlihpp iSh$>, lihQp IpiuiuiGiuGp huilpurpupd uipiuqnipjuiQ Ipmqp nu]pri uipuiqrupjiuQ hhui. 



1+'^ 



l+s-i 



1 + s- 



(1.7 - 10)-ni[ inpipiifr puiGiudLhpp pu&hpul mripq uipuiqnipjniQQhpp Glpxiiniiuiup , iSUGp IpiinuiGuiup. 



V = 


v' 


U 


u = 


u 


U 


w = 


w' 


1+4 


1 +S jf 


1+4 



llj GmhtunU (1.6 - 5)-ni[ inpipufr hiuiliuuiupnuiGtipp hunSuiquipqtipp uinuigpQ U hpqpnpq huiq'uiuuiprmSQhpp lihg 
inhrpunjitipuL (1.7 - 8)-ni[ U (1.7 - 9)-ni[ inpipufr yS qnp&iul}pgQhpp uipmuihujjuinipjniQQhpp, pG^iuhu QuiU oqimlhpiq' 
(1.3 - 30)-pg, lihQp IpauiuiGiuGp hhuiujiUL uinGyupjiuGGtipp. 



r(v') = 54(i + ^) 



r(v)--g^fi..x. 

d(v ) 



r(«') = -^-(i + *f) 



r(M ) = ^i(l l ,iL- 
d(w J 



7("')=-g4(l + ^) 

rf(w) L 



a(w ) 



1.7-10 



1.7-11 



1.7-12 



(1.7- 10)-p, (1.7- ll)-p U (1.7- 12)-p hiuiSiuinhri qppuinnnSpg iShGp IpnniuGuiGp htunhjuiL uinGyupjniGGQpp. 

r 



Y(v')v' = 



d(v) 



y(v)v 



y{u)u' = 



d{u) 



y(u)u 



y(w )w = 



d{w) 



y(w)w 



y(v)v = 



tf(v') 



/(v')v' 



d(w ) 



7(w)w = 



rf(w') 



7(w')w' 



f>piup hhin piuqiSiuupuuilp'jp 11 ! (1.7 - 10)-ni[ U (1.7 - ll)-ni[ inpipufr puiQiudUhpp, iShQp IpuiSiujuilpiiQ R> U w 1 mnjiri h 
huilpurpupd uipuiqrupjiuQ huiiiuip IpnnuiQuiGrj hhinUjiu^ uinQyupjniQp. 

(l+-^)(l+4) = l 
Oqini[hpiq' (1.7 - 10)-hg, iShQp GmjGuihu liuiuuijuilpuG w uipuiqrupjiuQ huiiiuip, IpunuiQiuQp hhuihjuiL uinQyupjruQQhpp. 



1 + 1'^ 



1 + -k?-^- 

2 C 



1 + ^-s-^ 

2 C 



1 + T^ 
l+.v-^ 



1+s^ + g- 



l+sf +g\ 

_ Cj_ 

(1+.^) 2 



^uuSiuinhii qppuinhpii[ (1.7 - 12)-p U (1.7 - 15)-p hpljpnpii. hiuiluiuiupnuip, iShQp IpuiSiujuilpuG w uipiuqnipjuiQ hiuiSiup 
IpunuiGuiGp hhuihjuiL Ipuphnp uinGynpjruGp. 



7(>0( 1 + T'4) =,,M( 



1 + i^) 



1.7-13 



1.7-14 



1.7-15 



1.7-16 



26-82 



Upui^uiq"! Injupp ^uipuipupuiquiQ CuipdiiuiQ ShumpjniQ 



(1.3 - 34)-p dhg uiDquiqpuniq' (1.7 - 8)-niJ U (1.7 — 9)-niJ uipiluift p qnpfruiqpgQhpp uipinuihuijinnLpjnLQQhpp, lihQp 
quniuijuiquiQ w u w' mqpq U huilpiiquipd uipuiqnipjniQQhpp huuSuip quuiuiQuiQp hhuiujuq uinQyupjniQp. 



y(w)y(w') = P(w)P(w') 



l+.v- 



1+.S-J 



[+sJ F + ! 



1 



> 



1 +,-*-+, 



1 



WW 

8 c 2 



(1.7 - 17)-fig hhmLnuS t Quili, np IpiiuuijuilpiiQ w U w mqfiq u huiquiquipd uipuiqmpjuiQ huiuuip iip2in inuqp mQp 
htunLjuiL umQyupjmQp. 



< 1 



bph uijdu (1.3 - 28)-ni[ u (1.3 - 31)-ni[ inpi[ui& npn2p£p uipuiuihuijuimpjniQQDpp uqj inuquiqpDQp jS(v)-p 
uipinuihuijinnLpjmQp (1.7 - 8)-pg u /?(v')-p uipuiuihuijuimpjniQp (1.7 - 9)-pg, pQ^iquu QuiL ilDphf^Qpiil (1.3 - 29)-p U 
(1.3 - 37)-p, uiupu uuQp d(v) U d(y') npn2p^Qhpp huniuip IpnnuiQuiQp Quili hhuiujuq puiQuiduupp. 

rf(v , ) = r 2 (v , )(i + ^)(i-gfr)*° 



< 



^) = r 2 (v)(i + .^)(i-g^)*o 
^) = r 2 (v)(i + ^ + g^-) *o 



< 



d(v) = y 



(v')( 



l+s^+g^ 



9 



* 



fqiuip hhin puiquuiunuuiqtqnq' (1.7 - 19)-ni[ inpipufr huuluiuuipnuiQhpp huiuuilpupqhpp hpqpnpq huuhuuuipmuQhpp h 
uij Qmhhuih oqinqMipiq' (1.3 - 30)-pg h (1.7 - 17)-pg, uhQp IpiuiuiQuiQp hhuihjuqhuiuui^uiqh uinQyupjmQp. 



(i + .vx + ^)(i + .4 + ^)^(i- g ^) 2 



Ujdii (1.3 - 35)-niJ uipq\u& qpiuqiuQ h puiguiuuilpxiQ 6UunpnJunipjnLQQhpp iquijuuiQh uh$> inhquiqptqni[ IpnuuijuilpjiQ w 
uipuiqmpjuiQ huniuip /3(w) h fS(w' ) qnpdwqpgQhpp mpmwhwjmnLpjniQQhpp (1.7 - 8)-pg h (1.7 - 9)-pg, pQjujhu Quih 
4hphp2tipiil (1.3 - ll)-p, lihQp buuiuiQuiQp hhuiujuq Qnp unujuuiQQhpp. 



^puiquiQ duuiqhntunipjmQQhp 



PuiguiuuilpiiQ dUuiqhnJumpjnLQQhp 



l+sf- >0 
l+s*f > 



l+sf- <0 

l+S^r- <0 



1.7-17 



1.7-18 



1.7-19 



1.7-20 



1.7-21 



llj QmhhinU oqunlhpnl (1.7 - 21 )-n4 uipiluift qpiuqiuQ - puiguiuuiquiQ dUuupnhmipjniQQhpp Qnp upujuuiQpg U 
(1.7 - 17)-ni[ inpipufr uinQyupjmQpg, Ipupnq hQp hqpuilpiigQtqnp quniuijuiquiQ uipuiqmpjuiQ hiuiiuip qpuiquiQ h puiguiuuilpxiQ 
duuiqhntunipjniQQhpp ujuijuuiQp uhQp quipnq hQp qptq Quih uhuiuhQ hhinLjuiL Iphpiq. 



QpiuqiuQ duuiqhntunipjmQQhp 



PuiguiuuiquiQ dUuiuinpinipjniQQhp 



1+sf- > 



1+s-f <0 



1 +s- 



■ + g- 



> 



1 +s- 



+ g- 



< 



1.7-22 



Oquiq'tqnq' (1.7 - 19)-n4 uipq'uicJ huiqMuuuipnuiQhpp huiuuilpupqhpp uinuigfiQ huuluiuuipnuiQhppg, pQ^ujbu QuiU 
huiuuiduijQ (1. 1 - 20)-fi U (1.7 - 22)-{i, qpuil}ui(i U puiguiuuiquiQ dUuiq^nJunLpjniQQhpp ujuijiiuiQp, uhQp l}uipnq hQp npn2tq 
y(v) U y(v') qnp&uiqpgQhpp uipinuihuijinnipjniQQhpp qpuiljuiQ U puiguiuuiquiQ dUuiq^npanipjniQQhpp huuSuip htunUjun qhpu}. 



< 


O-puiljuiQ dUuiq^nJunipjniQQhp 

r My) 

v(v) - v > 


PaigaiuiuliiuQ dUiui]inliinLpjnLQQhii 

rM - ^ > o 


Jd(v ! ) 

r( V ') = v > o 


H 1+t * +s $) 


f^ > 





1.7-23 



27-82 



4,uijl}iuliuiQ <uipiuphpuil}iuQnipjuiQ ^uiinmlj ShunipjniG 



EGqq&md 1-12 - 0tJihiS tptpwdwbwG t (1.7 -23)-/ ilbp nGqmGbi d(v) = ±1 (hmii np GnijG t pGnniGty d(v') = ±1) 
b iSbGp hh/wmpjwrfp bwpnq bGp npn^b[ y(v) qnp&wbgp wpdbpp (bwiS y(v') qnpdwljgp wpdbpp): fiwjg rffiGjb dhpp 
UGbbqfr ipGbpu hwiSwp wbinp t wub[ np d{v) = ±1: pGqniGbpupjmGp bwdwjwbwG t b jfi pfumiS (1 - P-)-nd mpdwd 
■CwjbwqwG hwpwpbpwbwGmpjwG hwinmb inbumpjwG hpdGwqpmjpGhppg: 4bmbwpwp y(v) qnpdwl/gfi wpdbpp qmGh[m 
hwtlwp UbGp wbmp t npnGbGp iSbl] wji tfwGwwwph, npp ppJp dbp hwpwphpwlpiiGmpjwG hpdGwqpmjpGhppg: 

Oqinqbmq (1.6-7)-nil, (1.6-9)-nil, (1.6- ll)-nil, (1.6- 13)-nil, (1.6- 15)-nqL (1.6- 17)-nq uipquift 
hiuihuuiupnuiQDpp hiuiSiulpjipqDpp iniupiufrmpjiuQ dluuipntumpjiuQ huiiluiuuiprmSQhppg U hpljpnpq huii[uiuuipnnSQhpp 
puiduiQhpi4 uiniujpQ huuluiuuipmiSGhpp ijpiu, pd^upju Quih oquiuiqnp&tqml (1.7 - 8) -ml U (1.7 - 9)-ml inpihud puiQiudUhpp, 
iShQp IpiimuQuiQp mqpq U hiulpuqujpd hiupiuphpuilpuQ lupiuqmpjmQQDpp iSpjU qnjmpjmQ mGhgnq prqnp hphp 
umQjnipjniQQhpp: 

♦ (1.6 - 11) -nd b (1.6 - 9)-ni[ inpdw& mwpwdmpjwG dbwipnpjmpjwG hwdwuwpmdGbppg, iSbGp buiniuGwGp 

w mqjiq lupiuqmpjuiG hunSuip w' hiulpuqujpd ujpuiqmpjuiQ huiiiiup 

u + v + s^- , u' + v' + s^- 1.7-24 

w = ttt^- U w = j—r — 

L c 

♦ (1.6-15) -nd t (1 . 6 — 7) -ni[ mpdwd mwpwdnipjwG dbwipnpjmpjwG hwdwuwpmdGbppg, iSbGp buiniuGwGp 

u mqjiq lupiuqmpjum hunSuip u hiulpuqujpd uipiuqmpjiuG huiiiiup 

w + v' + s^- , w' + v + s^- 1.7-25 

U = t—X ll U - r= 






♦ (1.6-13) -nd b (1.6- 17) -nd uipdwd wwpwdmpjwG dbwipnpjmpjwG hwdwuwpmdGbppg, dbGp 
bumwGwGp 

v mqpq lupiuqmpjiuQ huiiiiup v' hiulpuqiupd lupiuqmpjiuQ huiiiiup 



1.7-26 



1-gJLXL l-g^r 

c c 

Oquiiltqml (1.7 - 10)-ni[ uipi[iu& hujl}uiquipd lupiuqmpjmQQDpp Ipuii (1.7 - ll)-ml uipipu& mqpq lupiuqmpjmQQDpp 
puiQuidlihppg, lihQp (1.7 - 24)-ni[, (1.7 - 25)-ml U (1.7 - 26)-ml inpipufr lupiuqmpjiuQ dUuupnJunipjuiQ piuQiudlihpp, puin 
uiQhpuidh2UinipjujQ, Ipxipnq hQp lupiniuhiujintq Ipxui lipiujG mqpq lupiuqmpjmGuQpml U liuui tq lipuajQ huiljiuqiupd 
lupiuqmpjniGGQpml JiQ^iqhu gmjg t uipipu& uuinpU: 

♦ (1.7-25)-^ wpmwhwjmdwd dpwjG mnpq t/wd ilpwjG hwbwqwpd wpwqnipjmGGbpnd, bJpGp 
u mqpq uapuaqmpjuiQ huuSuap u hualjujqujpd uipuiqmpjuaQ huuiujp 



1.7-27 



♦ (1.7 -26) -p wpwwhwjwdwd dpwjG mqpq Ijwii dpwjG hwbwqwpd wpwqmpjm GGbpnd, IqpGp 
v mqpq uipiuqmpjuiG tuuiSiup v' hmljujqujpd uipujqmpjuaQ huiiiiup 



1.7-28 



l +sf+g jm. l+s jf +gJ ^f 



c" 



(1.7 - 24)-p duihi l}nqiip huuluauuipmiip lihQp Ijuipnq hQp huuiuiptq npu}hu hplpu mqpq ujpuiqmpjmQQhpp qmiiuipiSuiQ 
puiQuidli, npp Ijiupnq hQp qph^hhuiUjuq Ijhpuj. 



28-82 



Upuj^uiip Injhpp ^uipuiphpiuquiG CuipdiiuiG ShumpjiuG 



w — u ffi v = 



1-g- 



t>ulj (1.7 - 27)-p duipj Ipiipip hiui[iuuiupnLiip lihQp quipnq hQp huiiiiuph^ npiqhu hplpu nu]pq ujpuiqnipjniQQhpp huiQiiuiQ 
puiQuidU, npp Ijiupnri hQp qph^hhuiUjun l}hpu[. 



l+st+g**- 



1.7-29 



1.7-30 



CQllq&nuI 1-13 - (1. 1 - 29) -ni[ h (1. 1 - ?>0)-ni[ wpijwd wpwqmpjniGGhpp qnirfwprfwG h huiGiSuiG puiGwdhhpp rfhGp 
Gwpnq tpGp uwiuGwi GwL {1.5 -l)-p h (1.5 - 6)-p wniuppG hwilwuwpmiSGhppg, wjGinhq whqiuripbinil /J(v) qnp&whgp 
wpdbpn (1.7-8) -fig: 



(1.6-7)-ml, (1.6-9)-nq\ (1.6- ll)-ml, (1.6- 13)-ni[, (1.6- 15)-nilU (1.6- 17)-nil inpipufr hunlunuupnuiQhpp 
hiuiSiulpjjpqhpp iniupiudnipjuiG 6UunpnJunLpjniQQhppg uimugipiifr umuigpG hiui[iuuuipiiuiQ uipiniuhiujimupjiiiGGtippg iSUGp 
quuiuiGuiGp y qnpfruilipg Qhpp pnpip hGiupim[np dLunpntuiupjiuGGhpp, npnQp iSpumpG qpipiid IppGhG. 

i) r(v ) = 7 («')r(w)(i-g^f) 

2) r( „) = r (v')r(w)(i-g^f) 

3) y(w) = y(v)y(u)(l-g^f 



< 



4) r ( v ') = r(«)r(vf')(i-g i ^) 

5) jiu') = y(v)y(w'){\ - g^- 

6) y( w ') = r ( v ')y( u ')(l-g^f 



Oquiq'hpiq' (1.6 - ll)-ml, (1.6 - 13)-ni[ U (1.6 - 15)-ni[ inpipufr himliuuiupnuiGhpp hiuiSiulpjjpqhpp duiiSuiGujljp 
dliUiq^npanipjniQQhppg uiniug0 1 ui& uiniujpG huiqMuuuipiSuiG uipuiuihuijuinipjiuGGtippg lihQp y qnp&iul}pgQhpp huiiiuip 
quuiuiQuiQp hhuiUjunhQuipiuilnp dUunpnJumpjnLQQhp, npnQp lipuiupQ qpipufr IpJiGhG. 

1 



) r(v)(i + *£) = r(«')r(w)[(i + *-£)(i + *-*-) - g-^f ] 

2) y(«)(l + jf) = /(v')r(w)[(l + *4)(i + s*-) - g^f- ] 

3) r(w)(i + *-*-) = r(v)r(«)[(i + *£)0 + *-£) - *-)£■ ] 



"bmjQiqhu oquiqMipiil (1.6 - 7)-nq\ (1.6 - 9)-ni[ U (1.6 - 17)-ni[ inpipufr himliuuiupnuiGhpp hiuiSiulpjipqhpp diuiSiuGiuljp 
dUuiq^npanipjniQQhppg uiniugU 1 iu& uiniujpG hiuqMuuiupiSiuG lupuiiuhiujuimpjniGGhppg lihGp y qnp&uiljpgGhpp huiiiuip 
IpjuiiuGuiQp hhuiUjunhQuipujq'np dhiuipnJunLpjnLGGap, npnGp lipuiupQ qpipufr IpJiGhG. 



4) r(v')(l +*-£) =7(u)y(w')[(.l+sf)(l+s^-gJ^] 

5) r(«')(l+^) -7(v)7(w')[(l+.v^)(l+.s'^)-gJ^] 

6) r(w , )(i + ^) = r(v')r( M , )[(i + ^)(i + .s'4)-^^f] 



(1.7 - 32)-p U (1.7 - 33)-p hiuiliuuiupnuSGhpp piudiuGhpii[ (1.7 - 31)-ni[ inpipiifr hiuiSiuupuuiiuiiluiuG huiqMjJuuipnuSGhpp 
i)pui, lihGp IpiuiiuGiuGp hhuihjiUL lunGyupjiuGGhpp. 



* c 2 

( 1+ ,4) (1+ , 1) _ g ^ f 

1 + .$4 = ; C — 



1) l + ,£ = 



2) 



3) 1+sf 



(l+sf)(l+sf)-g 



Vlt 

,.2 



■*-f 



4) l+,s-£- 



5) 1+5 J 



6) 1+,^ 



(l+.vf)(l+.s^)-gi^ 
8 c 2 



1.7-31 



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2) 7W = -^y(v)y(w){\ + s^ + g^j 

3) rM = r(vW»)(i-«^) 



1.7-35 



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3) r(w)(i + *-*-) - r(v)r(«)[(i + *£)0 + *-«-) - *-jf ] 



1.7-36 



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1.7-46 



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1.7-47 



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x' = f(v)(x- vi) x = y(y')(x' - v't') 



1.7-48 



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1.8-10 



34-82 



Upuj^uiip Injhpp ^uipuiphpiuquiG CuipdiiuiG ShumpjiuG 



K U K mripq pQhpgpun huiiiuilpupqhpiuii 



K U K huilpjaijpp pGhpgpuiL hiuiiuilpiipqtipnui 



x — u t — 



(1.8 - ll)-nil npn2ipnfr uiuipui&nipjuiQ uinuiGgpiupiltipp lupdhpGhpp inhipxniphpiil (1.8 - 10)-p lihg, iSUGp IpnniuGuiGp. 
K U K pGhpgpuiL huiiiuilpupqtipp lipjU AT U K pQhpgpui^ hiuiSiulpjipqhpp iSpjL 



ft + 



ftf)( C 



$1 + 



^f)( c7 ) 



t(yO = (V+^t)(c?') 



f( c r) = (, 1 + , 2 f)(c?) 



1.8-11 



1.8-12 



(1.8 - 12)-p lihj, hpqpnpq huiqMjjuuipmiSQtipp puiduiGhpiq' luniujpG huiqMuuuipniiSGtipp djiiu, iShGp IpnniuGuiQp K h K 

— »' — > 
hiuquiqpp pGhpgpuiL hiuiSiulpjjpqhpnuS ipnpdQuilpuQ liuiuQpljp 2uipdiiuiG uipuiqnipjmQQhpp uipiniuhiujinU 1 ui& K U K niripq 

pGhpgpuiL hiuiiuilpxipqtipnLii GmjG ipnpdGuilpuG liuiuQpljp 2uipdiiuiG uipiuqiupjiuGGhpnil. 



JJl + IJ2- 



f/1 + I?2" 



<iun5hiSiuinhpiq' (1.8 - 13 )-ni4 uiniugiufr uiprymGpp (1.8 - 8)-nil inpipufr hiuquiqpp uipiuqnipjuiG puiGiudUhpp hhin, dhGp 
iSpuipdhpnphG quipnq hGp npryhL (1*1,^2) U (t)\,t]i) uiQhiujui qnp&uiljpgQhpp, npnQp liniQUQiuQ hhinUjun uipdhpQhpp. 



ft - 1 



iji = 

Jf2 = -1 



(1.8 - 14)-nil npn2ipn<* ^ 1± ?? qnp&uil}pgQhpp lupdhpGhpp inhquniphpiil (1.8 - 10)-p lihg, GhGp IpnnuiGujGp hplpu AT U 

K hiulpxirGip pQhpgpun huiiiujl}uipqhpnLii dinpdGiulpjjQ iSiuuGpqp uiGgui& dunJuiGuiqp U iniupiufrmpjuiG Ipiiiqp K U K nu]pq 
pGhpgpuiL huiiiuiljuipqtipnui GmjG ipnpdGuilpxiG iiuiuGpl[p uiGguifr diuiSiuGuilip U uiuipui&nipjuiG hhin. 



K U K pQbpgpun huiiiuilpiipqtipp lipgli 



K W K pGhpgpuiL hiuiSiulpjipqhpp iSpjL 



Ct = ct + sx 



ct = ct + sx 
x — —x 



(1.8 - 15)-pg GhGp IpnniuGuiGp K' U K mqpq U huilpurGip pQhpgpun huiiiiulpiipqhpnLii 2uipdd 1 nq UinpdGuilpjiG iSiuuGpqp 
dun5uiQuil}p U uiuipui&nipjuiQ ijp^hphQgpunQtipp htunLjuiL Iprnqp. 



K U K pQhpgpun huiiiuilpiipqtipp lipgU 

J cdt = cdt + sdx 
ax — —ax 



K U K pGhpgpuiL huiiSuiUuipqapp iSpjU 

J cdt = cd t + sdx 
dx — —dx 



1.8-13 



1.8-14 



1.8-15 



1.8-16 



Oquiq'hpiq' (1.8 - 15)-pg lihQp Ipupnq hQp npn2bt QiuU K U K mqpq pQhpgpun himSuilpjjpqhpnuS 2iupdilnii ipnpdQuil}iuQ 

iJiuuQplip uiQgiu& diuiiuiQiuqp U iniupiu&nipjiuQ l}iuu}p K U K hiuquiqpp pQhpgpui^ hiuiSiuquipqhpniiS QnijQ LpnpdQuiqujQ 
iSuiuQpqp iuQguj& duiiiuiGiulip U iniupui&nipjuiQ hhui. 



K U K pQhpgpun huiiiuilpupqtipp lipjU 



K U K pQhpgpun hunSuiqujpqtipp iSpjU 



Ct = ct + sx 
x — —x 



ct = ct + sx 



1.8-17 



(1.8 - 16)-pQ huiiiiuQiiuiQ, (1.8 - 17)-pg lihQp quimuQiuQp K' U K mripq U hiuqiuqpp pQhpgpun hunSiuqujpqtipnnS 
2uipdd 1 nq ipnp&GuilpuG iiuiuQpl}p duiiiiuQuilip U inuipiudiupjiuQ qp4)^>hpti(igpuip3hpp hhLtilijunl}iuu}p. 



35-82 



4,uijquiquiQ <uipiuphpuil}iuQnipjuiQ ^uiinniq ShunipjniQ 



K U K pGhpgpuq huiiiuiquipqQpp lipgU 

\ cdt = cd t + sctx 
dx — —dx 



K U K pQhpgpuq hiuiSuiquipqtipp iSpjL 

J cdt = erf f + .srfx 
rf? = -a*x 



Oqini[hpiil K' W K mqpq U huiquiqpp pQhpgpuq huiuuiquipqapnuS (1.8- 3)-ni[ U (1.8 - 4)-ni[ inpi[ui& q^inp&QuiquiQ 
uuiuQpqp lupuiqnipjniQQhpp uuihuuiQnuSpg, uhQp (1.8 - 16)-pg U (1. 8 - 18)-pg quipnq hQp npn2tq mqpq U huiquiqpp 
duiuuiQuiqQhpp qpq^GphQgpuqQQpp lipgh hqui& hhuihjuq quiiqp. 



K U K pQhpgpuq huiuuiquipqhpp lipgh 



K u K pQhpgpuq huiuuiluupqhpp up$>L 



it' = (l+S-^r\d~t' 
d~t' = (\+s-*f\d*t' 




1.8-18 



1.8-19 



Cuq.q&mu 1-18 - (1.8 - l5)-nU 6(1.8 -ll)-nU uuiiugdmd mpiyniGpGbpii Gnp imju bO uUinmrf $>pqfiljuijmil 
hwjmGwphpilw& hwdw^wipnipjwG pjuipjinduiG (P hwGw^iuipmpjwG JiiwfumGwG) ipwuuip dpw: 4wGwdwjG ■dujqwbwG 
hwpwphpiulpiiGmpjiuG hwmml] mbumpjwG, /y GbbuiwpwbuiG $>pqJihiulpiiG iSbdmpjmGGbpp (dwiSwGwbp, qwGqi[wdp, 
LwqpwGdpwGp b wjiG...) mwpwdmpjwG hwjbiwjpG ujGijpiuijujpddiud pGbpgpwi hwGwbwpqbpniG, p iniuppbpmpjmG tupqp 
$>pqpbwjp upuuiqbpwgiSuiG, qhnqhnfudniii ' bG: XjGwGwujbu hwjb{wjpG wGqpwqwp&GwG qbiqpmd dbqmnpwqwG fypqJiqwbuiG 
GbdnipjmGGbpp (mpmqnipjniGji, wpwqiugmGp, pwipp b wj[G...J, pwgp niqqmpjniGji 2fl2bpiig, qpwGg pwgwpdwb 
iShdnipjmGGhp[i GmjGiqbu UinUinpjdmd bG: fiul] npn2 fypqpqiubwG Gb&mpjmGGbp ' qnpdnqmpjwG pGmbqpuqji, tGhpqfiuiG b 
wjiG, hwjbiiujpG wGqpwqwpdiSwG qbuipmd GGniiS bG wGipnipnpj (hwdbidmir 2): 

X>2hQp np (1.7)-pq puidQnuS uuiuigiluifr prqnp puiQuiduhpp lihQp quipnq hQp qptq QmjQnipjuiup, upuijQ uijQ 
inuipphpmpjuiup, np mqpq uipuiqmpjmQQhpp huiuuip qoquiuiqnp&hQp mqpq 4kll mn I 1 P Q2uiQp, put} huilpuquipd 
uipuiqmpjmQQhpp ]muquiQ2UiQp q^npauiphQ qoqinuiqnpdhQp huiquiqpp ^blpnnpp Q2UiQp: 4uiuhQuijQ qhupi lihQp uiQhpuidh2Ui 
hQp huiuuipnui npn2 puiQuiduhp uhjphptq uijuinhq ilhliuinnuiquiG Q2Uiqpmpjuiup , npnQp lihQp oqinuiqnpfrtqm hQp uiju h 
hhinuiqui puidhQQhpnui: 

Q-phQp dhuidintumpjuiQ nprypjGhpp upjh (1.3 - 30)^4 uipq\u& uinQyupjmQp. 



d(j)d(v) 



1 



"bmjQiqhu qphQp (1.7 - 19)-m[ inpipxid huuluiuuipnuiGhpp huiuuiluupqhpp uinuigpQ huuluiuuipnuiGhpp. 





^<v) = 7 x 7 )( i+ 4 + ^)* 




<^)^ 2 ( v )( i+ 4 + ^)*° 



1.8-20 



1.8-21 



Q-phCip Qiuli (1.7 - 12)-m[ inp^uifr uinQjmpjniQQtipp l}aiuaijiul}ai(i w mqpq U hiul}iuqpp uipiuqiiipjiuQ huiiiiup. 




1.8-22 



l^Q^iqhu QuiU qphQp (1.7 - 13)-ni4 uipOjUift lunQ^nipjniQQtipp quiihujuiquiG w mqpq U hiuquiqpp uipiuqnipjuiQ hunSiup. 



y(w^\ 



d(w) V J 



y(w)w = — -?W-7(V)v 
d ( w ) 



1.8-23 



Q-ptiQp QuiU q' a 'l mn P al 'l ul Q Q2iuqpiupjaiup (1.7 - ll)-n\[ inp^uicJ hhinUjuq quiplaip uinQjnipjmQp. 



36-82 



Upiu^uiip Injapp <iupuipapuilnuG CiupdiiiuG ShumpjmG 



y(w)/(w) = P(w)fi(w~) = 



1 +s- 



1+s^ + g- 



1 +s- 



l+sf+g- 



> 



1-g- 



1.8-24 



Ujdii oquiijtqml (1.8 - 3)-nq\ (1.8 - 4)-ni[ U (1.8 - 5)-ni[ inpihufr G2iuGiulmuiGappg, qphGp (1.7 - 48)-nil uipihuft 

<uijlputpuG mupiupapuilpuGmpjuiG hiuuimli uitiumpjiuG mqpq U huilpuqiupd duiuipntumpjiuG huuluiuuipnuiGtipp 

— >' — > 
ilalpnnpuilpuG G2 uac U l mpjuiu'p, GpuijG K U K mqpq pGapgpuq hiuiiiulpxipqapp lipjU: 



1. 4iujl]wbmG dbwiprifumpjiuG hwilwuwpmiSGbpii K b K iSliwjG mqpq pGbpgpwi hwGwbwpqbpp Gp£b 



fliqpq dluuq'intumpjmGGap 

f/-r(v)[(i + 4)r + ^] 


u 


<uitpuquipd duuiipnpimpjniGGap 

* = r(v")(*' -v~t j 



1.8-25 



CQqq&nnI 1-19 - (1.8 - 25)-wpi/ui& mqpq dbwUinfiimpjiuG hiuUiuuiupmMbpp dbg bppiunhiml (1.8 - 2Q)-ni/, 
(1.8 - 21) -ni/, (1.8 - 22) -nU b (1.8 - 23) -m/ inpGmd puiGiudbhpp pum uiGhpwdb^uimpjmG, GhGp 1/uimiiGwGp 
( 1 . 8 - 25 ) -inpdwd hwl]wquipd dLuiipnpjmpjwG hwdwuwpmGGbpp: ^binbwpiup ( 1 . 8 - 25 ) -nd inpdwd mq/iq U hwliwqwpd 
dbiuipn[umpjwG hwdwuwpmiSGbpii ppbGg ilbp hwbiuumpjniG jbG upupmGwbmd: 

Ujdii lihQp guiGlpuGnui aGp uinuiGuq <iujquil}iuQ mupiupapuilpuGmpjuiG hiuuimq uiaumpjiuG (1.7 - 48)-m[ inpihufr mqpq 

U hiuquiqiupd duiuipntumpjiuG huuluiuuipnuiGtipp q'hquinpujquiQ Q2Uiqpmpjujiip, iSpiujG K U K huiquiqpp pGtipgpuq 
huiiSuiqiupqapp iSpjL: 'l-pui huiduip uiGhpuidti2in t (1.8 - 25)-m[ inpipufr mqpq U hiuquiqiupd duuuhnpimpjiuG 
huuluiuuipnuiGtipp iiti$> qppiuntq duiiiuiGiuljp U uiiupiu&mpjiuG (1.8 - 15)-ml U (1.8 - 17)-m[ inpq^uifr huijtquijhG 
uiGqpuiquipdiiuiG dhuiGinlumpjuiG hiuqMjJuiupmiiGQpp, pGjiqhu Guilt oqin^tq (1.8 - 20)-nq\ (1.8 - 21)-nq\ (1.8 - 22)-ml li 
(1.8 - 23)-m[ inpqMnfr piuGuidLappg puin iuGhpuidti2UinipjiuG: Ujq pnmpp Ipxunuiptqmg htunn lihGp quuiiuGuiGp hhuiUjuq 
dliUiq^npampjiuQ huiqMiiuuipnuiGtipp: 



2. -imjljuibiuG dbimpnfiimpjiuG hiudiuuiupmdGbpp K b K rfpuijG hwlpuqpp pGhpgfiuiihiurfiubuipqhpp rfppb 



fliqpq dUuiLpnpampjmQQtip 

<~' = r(v)(V-gj-$r) 

*' = r00[(i + 4>+^] 



hiuquiqiupd dUuiipnJumpjniQQhp 

~ = r(V)(V 



8 ^ 



<*)[( 



1 +s- 



VT<] 



1.8-26 



llnuiGdGuiqp htunuippppmpjmG t QapqiujiugQmiS qptq 4,uijquiqiuQ dLuuhnhvimpjuiG huiGjuuuipnuiGapp hiuquiqpp U mqpq 
pQhpgpuq huuiiuquipqUpp lipgU quid mqpq U hiuquiqpp pGhpgpuq hiuiiiuquipqtipp lipgU: flpiu huuSuip iSaQp, puui 
uiQhpuidh2UimpjiuQ, GmjOwtiu iqhuip t oquiqMiGp (1.8 - 15)-ml U (1.8 - 17)-ml uipinuft hiujhpujpQ uiGqpuiqiupdiliu& 
dlauq'inpimpjiuG huiGjiiuuipnuiGappg, pQ^iqhu QuiU (1.8 - 25)-niJ U (1.8 - 26)-niJ mpijuift 4,iujljuilnuQ dUiuq^ntumpjuiQ 
huu[uiuuipmiiQhppg: Ujuu[puni[ iSUQp IjuinuiQiuGp hhuiUjuq dUiuipntumpjiuQ huu[uiuuipmiiQtipp. 



3. ^wjljuibiuG dhwipnlvmpjiuG hwGwuwpniiSGhpii K hwbwqpp U K niqpq pGbpgpwi hiuiSwliwpqbpp iSpgh 



7' = r (?)[7 + (s + g i-)p] 



-r(v")f/-V? J 



1.8-27 



37-82 



4,uijlpuquiQ -iuipiuphpuilpuQnipjuiG ^imnniAj ShuiupjniQ 



4. <Ziujl]wliiuG 6biuipn[umpjwG hwGwuwpmiSGbpn K mqpq b K hiubwq[ip fiGbpgpwi hwiSwbwpqbp[i iSpgb 



x — -y 



00[(i+4)* + ^] 



t = y 



(v){(i+4)"' + [ 5+(s2 - g) ^]^'} 

r(v)[(i + *l)^' + VV'] 



QGqq&md 1-20 - (1.8 - 25)-nG, (1.8 - 26)-/»/, {\.%-21)-nGb{\.%-2%)-nGwpGw&<wjbwbwG6bwipnpjmpjwG 
hwGwuwpmiSGhpn iSbGp bwpnq bGp qpb[ Gmb wpiniuhwjinGw& l]iuiS iSpwjG v niqpq hwpwpbpwljiuG mpuiqnipjunlp bwiS 
d/iwjG v hwbwqpp hwpwpbpwl]iuG wpwqnipjwGp b bwG t[ npbt iuji mwppbpwl]nil: 

llpdh i^hl[innpiul[UjQ Q2iuqpnipjunS qpht QiuU uipuiqnipjniQQhpp qnuiuipiSiuQ U hiuGiiuiG puiGiudLhpp: ^pui huiiiiup 
uipiuqnLpjmQQtipp (1.7 - 24)-n4, (1.7 - 25)-ni[ U (1.7 - 26)-ni[ inpipufr puiGiudLtipp iSq$> qppuinhpii[ nii]pr[ U hiuquiqpp 
i[tlpnnpiuquiQ Q2iuqpnipjmQp, lihQg quimuQiuQp. 



♦ UpiuqnipjmGGbpfi qmiSwpiSuiG puiGw&bbpn 

w mqpq lupiuqmpjuiG hunSuip 

v u 



u + v + s- 



w — 



1-*- 



w hiuquiqpp lupiuqnipjuiG hunSuip 



1-g- 



1.8-28 



1.8-29 



♦ UpwqmpjniGGkpp hwGiSiuG pwGwdbhpp 
~u mqpq uipuiqnipjuiG hunSuip 



w + v + s- 



l- g . 



u hiulpiiqpp lupiuqmpjuiG hunSuip 



W + V + s- 



l-g. 



1.8-30 



♦ UpwqmpjniGGkpp dbmifinfuGuiG wji [pwgnigfy pwGiudbbpp 



v nuipq lupuiqiupjiuG hunSuip 



v hiulpiiqpp lupiuqmpjuiQ hunSuip 



w + u + s - 



l-g- 



w + u + s - 



1-8- 



1.8-31 



f'ulj (1.7 - 31)-ni[ inpipufr pnpip y qnp&iulipgQhpp 6UunpnJunLpjniQQhpp lihg GmjGu[QU qppuinhpii[ nu]pri U hiuquiqpp 
iJbqinnpuiqujQ G2iuqpiupjiuGp, lihQp IpiuiuiQiuGp. 



i) r(v) = r(«)/(w)(i- 5 ^f) 

2) r(«) = r(V)r0i0(i-^f) u 

3) r(w) = r(v)/(T?)(i- g ^f) 

Oquiq'hpiq' (1.8 - 30)-pg U (1.8 - 32)-pg lihQp u niripri U huilpuiipp uipuiqiupjiuGGtipp huiiiiup IpiinuiQiuQp 

r(") = r(V>(w)(i-g^f) fr(«)=r(7>W(i-«| 

y(~ui~u = y(*v)y(wi ( w + V + s-^r- ) yCuju = y Qvjy (w~) I w + ~v 



4) r(V) = r0DrCO(i-^f) 

5) r(«) = r(v)r(t?)(i-^) 

6) r (V) = r (V>(V)(i-g^f) 



1.8-32 



1.8-33 



38-82 



1.8-34 



Upui^uiqi Injhpp <uqnuphpuiquiQ CuipdiiuiQ ShumpjniQ 



"buuiQuiuphu oqinqMipiq' (1.8 - 29)-pg U (1.8 - 32)-pg uhQp w mqpq U huiquiqpp ujpuiqnipjniQQhpp huniuip quinuiQuiQp. 

bqpiuljiugnLpjniQ 1.8 - (1.8- 15) -nif 6(1.8- 17 )-n if inpifmd dhwipnfumpjwG hiuifmumpniGGbpp hwGqpuwGmil hO 
iuG2iupd pGbpgpwi hwiSwbwpqbpp b qpiuGg hwjbiwjpG iuGqpwqwpdGw& pGbpgpwi hwiSwbwpqbpp iSpgL 4wjuwbwG 
dbwifinfunipjwG hwifwuwpmdGbpp: hub (1.8 - 25)-nif, (1.8 - 26)-mf, (1.8 - 27 ) -nif h (1.8 - 2%)-nif mpifwd dbwifinfunipjwG 
hwifwuwpmiSGbpp hwGqpuwGmu" bG bpbm 2wpdifnq pGbpgpwi hwiSwbwpqbpp iSpgL 4wjbwbwG hwpiupbpwhwGmpjwG 
hwmmb mbumpjwG niqpq b hwbwqwpd dbwipnpjmpjwG hwifwuwpmiSGbpp jnpu iniuppbpwbGbpp: 



1.9 - ^uipuiphpuiljuiQnipjuiQ ^Jn5Quir] : ]inijp]i Oquiuiqnp&nuSp 

cfuiiJuiQuiljuiuiuipui&nipjuiQ U]i2uiquijp]i ^ui2i]iSuiG -^uiiSuip 

UpqhQ uhQp uiutq tpQp h pQ^uphu qui hhinlduii t QuiU (1.8- 25)-ni[ inpi[ui& ^uijquiquiQ huipuiphpuiquiQnLpjuiQ huiuimq 
inhumpjuiQ duuidpnpinLpjuiQ huuluiuuipnuSQhppg, uhq liQnuS t npn2tq upuijQ y(~vj U yCv) qnpfruiqpgQhpp: ^pui huniuip 
uhq uiQquiu hu uhQp uphinp t oqinilhQp (1 -PJ-nq 1 inpq\u& hfiuQuiqpmjpQhppg, pphQg unihQuquijQ pQqqpqrmSnq': 

\>ui{u oquiq'hQp (1 - P)-n4 inpq'iucJ hpqpnpq hpuQuiqpmjppg, huiuuiduijQ npp duiuuiQuiqp pnpip pQhpgpuq 
huiuuiquipqhpnLiS «hnunui» t lipUQmjQ uilihqhpuiquiQ huiuuiuiinniQ c uipuiqnipjuiup u QhpqpuiqMiQp duiuuiQuiqp qM^puiguiquiQ 
up uinuiQgp, npp mQp hpquipmpjuiQ juiQinquiquiQnipjniQ, mqq^uifr t ilbiqp uiupuquiQ h npp uiuipui&nipjuiQ x uinuiQgpp hhui 
qwqunui t quiuwjmqwQ wQqjniQ, quipiqxufr t s u g hmumuiimuQ uhfrnLpjmQQhppg: 4,hinuuipuip uijq Qnp uinuiQgpp 
uinuiQgpuipqMjpp K 1 u K niqpq h huilpuqpp pQhpgpuq huiuuilpxipqhpnLU uhQp quipnq hQp uipuiuihuijuitq duiuuiQuiljp lipgngnq 1 
hhinhjuq qhpup 

K U K mqpq pQhpgpuq huiuuiquipqhpniu K U K huilpuqpp pQhpgpuq huiuuilpupqhpnui 

{x o = C t I dx a — cdt | x o = C t 

-, -> 1 -> ^ i<_<- 

X o = C t dxo — cdt x o = Ct 

Oquiuiqnp&hpiq' (1.9 - l^nq 1 inpq'uicJ Q2UiQuiqnuiQhpp (1.8 - 25)-ni[ h (1.8 - 26)-niJ uipijuift 4,uijquiquiQ mqpq U 
huiquiquipd dhuiq^npampjuiQ huiq'uiuuipmiiQhpp uhj, QhQp qpuiQp quipnq hQp qph|^ hhuihjuq qhpuj. 

1. AiujbiulpuG dbmipnfumpjiuG hiuifiuuiupmiiGbpp K h K mtipij pGbpgpwi hiuiSwGiupqhpp rfppb 

fliqpq dhuiipnhinipjniQQhp huiquiquipd dhuidpnJunipjniQQhp 

f = r (v) [(i + sf)*Wl?] ! J"o = r(V)[(i + .s4)?; ) + g^'] 19 . 2 

■iiujbmbmG dbmipnfunipjmG hmifmumpmiiGbpp K h K hwbiurjpp pGbpgpwi hmiimbmpqbpp ilpph 
Hiqpq dhuidpnJunipjniQQhp <uiquiquipd dhuupnJunipjniQQhp 

x' = r(v)(5 -gf-x) J Xo = r(v)(*o-,?-^-*'J 1.9-3 

x' = r(v)[(i + 4)x- + |x-„] iJ 1 !^= r (V)[(l + 4)x-' + lx-;] 



39-82 




1.9-1 



4,uijlpuquiG -iuipiuphpuilpxiGnipjuiG ^imnniAj ShuiupjiuQ 



\>iJuiGuiiqhu (1.9 - l)-ni[ inpipufr Q2iuQuil}niii(ihpp oquiuiqnp&hpii[ (1.8 - 27)-ni[ U (1.8 - 28)-ni[ inpipiifr ^uijquilpiiG 
dliUiipnpimpjuiQ hiui[iuuiupniiiQtipp iShj, lihQp qpuiGp quipnq hGp qph^ hhinLjuiL qhpiq. 



3. -iwjbwbwG dbwifin/unipjwG hwi/wuwpmGGbpii K hwuwqpp b K mqpq pGbpgpwi hwrfwbwpqbpp iSpgb 



t' =-r(v)(t-^ J 



x<> = 7 
x = -y 



(v)(t'-l: 



1.9-4 



4. ■(wjbwhwG 6bwipn[umpjwG hwGwuwpmiSGhpii K mqpqb K hwuwqpp pGbpgpwi hwUwhwpqbpp uppb 

?'o - r(v) {(1 + ,s4)x„ + [.s- + (s 2 - g)f ]*} J ?„ = 7 (V) {(1 + s ^y o + [s + (,v 2 - g )^y\ 

<v)[(i + 4)t + i^o] ? = - 7 (v)[(i + 4)v + i < f; ) ] 



x = -7( 



1.9-5 



lljchi AT' U AT mqpq U huilpuqpp pGhpgpuq hiuiiujlpiipqhpp uihuujGljjiuGpg qpinuipghGp L GlpiipiuqphGp hplpu 
quiiiuijiuqiuQ Tl\ U ^2 iquiuiuihuipGhp, npnQp mGhG htunLjuiL chuiSuiGuilpiiinuipiu&uijpG uinuiGgpuipqMjpp: 

♦ 'UwwwhwpGbpp wnwGgpwpUbpii K h K mqpq pGbpgpwi hwiSwGwpqhpmil 
"l l iquiinuihuipp uinuiQgpuipilhpp ^2 ujuiuiuihuipp uinuiGgpuipilhpP 



K pGhpgpuq huiiiuilpxipqnui => fx^o.x^ij 
K pQhpgpun himSuilpupqnuS => (x t l0 ,x t ij 



K pGfcpgpuq huiiiuilpupqnui => (x^o.-*^) 
K pGhpgpuiL himSuilpupqnuS => (x^Oj-*^) 



1.9-6 



♦ 'UwwwhwpGbpp wnwGgpwpGbpp K b K hwbwqpp pGbpgpwi hwrfwbwpqbpmiS 
"l l iquiinuihuipp uiniuGgpuipilhpp ^2 ujuiuiuihuipp uinuiQgpuipilhpp 



K pGbpgpuq huiiiuilpxipqnui => (^10,^1) 
K pdhpgpuiL hiuiSiuquipqniiS => (x~ l0 ,x~ij 



K pGfcpgpuq huiiiuil}iupqniii => (^20^2) 
K pdhpgpuiL hiuiSiuquipqiuiS => (x~ 20^X2) 



1.9-7 



bplpu "li U ^2 upuuiuihuipGhpp (1.9 - 7)-ni[ inpipufr huilpuqpp uiniuGgpuipilhpP uipinuihuijinU 1 ui& (1.9 - 6)-nU 1 uip^iuft 
mqpq uiniuQgpuipq'tipnq', hunSiudiujCi (1.8 - 15)-p, IpuGhGuiG hhinUjun umGyupjiuGGhpp: 



♦ K L K pGbpgpwi hwiSwhwpqhpp iSppb 
(T 1. upuuiuihiupp huiiiuip 



-10 — ^lO 1 ""] 



- 1 — — ■* 1 



4l 2 iquiuiuihuipp hiuiSuip 



► 20 — •* 20 " 



1.9-8 



♦ K b K pGbpgpwi hwrfwbwpqbpp Gfipb 
(T l l upuuiuihiupp huiiiuip 



X 10 - x 10 + SX 1 
X 1 = —X 1 



< T 1 1 iquiuiuihuipp hiuiSuip 

J x lb ~ X 20 + .VX 2 
X~ 2 = ~~X2 



1.9-9 



40-82 



Upuj^uiip Injhpp ^uipuiphpiuquiG CuipdiiuiG ShumpjiuG 



M^tqhu GuiU uijq QnijG hplpu ^i U ^ ujmmmhwpGhpp dmdmGwqp U mwpwdmpjwG wnwGgpwpilhpp 
iniupphpiupjiuGGhpp K' U K nu]pq U hiulpjjqpp pGhpgpuiL hiuiSiuquipqlipiuiS G2iuGuil4tiGp hhtnUjui^ Ijhpuj: 

♦ K b K mqpq pGbpgpiui hiudiulpupqbpmd 

ll i l U Tl 2 upuuiuihuipGhpp uinuiQgpuipiJhpp iniupphpiupjiuGp 

K pGhpgpuiL huiiiuilpupqnui => ~x 20 - ?io = 7 = Ct U ~x 2 - "x \ - ~x 1.9-10 

K pGhpgpuiL huiiSuilpjjpqnuS => x 20 - x w = xo = ct U x 2 - X\ = x 

«— 

♦ K b K hwlpuqpp pGbpgpiui hmiimbmpqbpmii 

r7 l l U Tl 2 upliuiuihujpGtipp umuiGgpujpqMjpp iniupphpiupjiuGp 

K pQhpgpun huiiiuilpupqnui => *x 20 - ^10 = ^0 = Ct U 'x 2 -x~ \ = x~ 1.9-11 

K pGhpgpuiL hunSiuquipqimS => x 2 q - x 1() = xo = c t U x 2 - X\ = x 

(1.9 - 10)-ni[ U (1.9 - ll)-ni[ inpipufr hplpu tr l\ U ^2 upiiinuihuipGhpp mqpri U huiljiuiipp uinuiGgpuipq'tipp 
iniupphpnipjuiG Ipmqp, hunSuidiujG (1.9 - 8)-p U (1.9 - 9)-p uipOjUift hG uinnpU. 



K U K pGhpgpun huiiiuilpupqhpp dpjU K U K pGhpgpui^ himSuilpjjpqhpp GpjL 




X() = X() + sx 

<— — » 

X = —x 



UuiMmQnuI 1-3 - bpbm K' b K mqpq b huibiuppp pGbpgpiui hwiSuibwpqhpmil XI. 9 — 6)-nif b (1.9 -l)-nd mpduid 
bpljm upuuiwhwpGbpp rffipb bqwfr dimSwGwbimmupwdwjpG «hbniui[npmpjmGp», npp bwpjdwd t GpwjG dwiSwGwbp b 
mwpwdnipjwG wmiiGgpwpdbppg, iSbGp biuGdwGbGp iSpgwbwjp b bG2iuGwbbGp mjG ^wjbmbwG «h» wwnni[, npp 
hwtSwdwjG (1.9 - \0)-nd b (1.9 - 11) -nd mpduid G^wGwbmtSGbpp, wiShGwpGqhiuGmp pwmiibmuwjpG wpmwhwjmmpjwGp 
bniGbGw hbmbjwi mbupp. 

♦ K b K mqpq pGbpgpiui hiudiulpupqbpmd 

— >' — *'2 /_>' _j' \ 2 / ./ .; \ / j .! \ / j .! \2 . n j .> .12 

K huiiiuilpjapqnui => 6 = ^"f *20 _ *io ) + A[x 2a - x m )(x 2 - x ^ ) + B[x 2 - x \ ) = Fx Q +Ax x +Bx >0 
^f himSiuquipqnuS => b = F (x > 2 o - 3?io ) + j4(x ? 2o - ^10 ) (-?2 - ~x\ ) + B(~xi - ~x\ )" = Fx () + A~xa~x + B~x >0 

♦ K b K hwbwqpp pGbpgpiui hiuiSwbwpqbpmiS 
K huiiiuiljuipqnui => b - F[ < x 2 o ~ x~ 10 J + A{ jc 2 o - -^io )(^ 7 2 - -^1 ) + B( ^2 - -^1 ) = F*x~a + ^^ox 7 + fix 7 >0 
K huiGuiqujpqniG => b = fCxio ~ *x 10 J + j 4(5 r 2o - ^10 ) 0*2 - ?i) + bCx 2 - ?i) = F^o + A*xqx + B*x >0 

flpinhri A, B \l F qnp&iul}pgGhpp diuGiuGuiljuiinuipui&nipjuiG lipgiuq'uijpp pGnipuiqpnq huiuuiuiuiniG Gh&mpjniGGhp hG 
U pGuiljuiGuipuip qui[uq'iu(y jhG hiupiuphpuil}iuG uipuiqnipjniGGhppg: Uju Gnp qnp&uil[pgGtipp iSUGp GnijGaibu iqhuip t 
npn2hQp, iupuiuihuijuihpii[ ijpuiGp dunSuiGujl}iuinuipui&nipjuiG bpljpuj^uiq^uiljuiG l}uinnig0 1 ui&pp pGnipuiqpnq U iShq uipijUG paii[ 
hiujinQp s U g huiuuiuiuiniG lih&mpjnLGGhpnil: 



1.9-12 



1.9-13 



1.9-14 



41 -82 



4,iujlpulpiiQ -iuipiuphpiulpuQiupjiuG ^luinmlj ShunipjiuQ 



CQqq&nnI 1-21 - Ubp uiwinl]hpwgi!uii!p, bpl/m ii]wimuhwpGhpp iSpph bqiud b (1.9- 13) -ni/ b (1.9- 14) -nti wptiuid 
piunmbmuiuj[iG wpinwhiujinmpjniGn iSfew iqbinp t ifiGp qpwbwG iSh&mpjmG, npnq'hbmb wjG hwGqpuwGmu" t bpbjiuip 
diurfuiGwliiuwiupuidmpjuiG rfhp bpbm bhwhpp rffipb bqiud hbmutinpmpjiuG piuniubmufiG: hub luUhifi Upp hbuuuqnuinqGbpp 
pnq 2iupmGwbbG b ipwgGbG Gbp piug pnqiu&Gbpp nGnniGbinq" np i[bpnh[i2J w L piunwbmuwjpG wpmwhwjmmpjmGp bwpnq 
IpGbi Gwb pwgwuwbiuG iSh&nipjmG: 

K' U K ninjiri U hiulpunpp pQhpgpiUL hiuuiulpupqapp inhuiuQlijniQpg, hplpu upuiniuhiupGapp upgU hrpu&, (1.9 - 13)-ni[ U 
(1.9 - 14)-ni[ inpipufr upjiulpujpapp piuniulpuupQ, hiuuiudiujQ (1 - P)-ni[ inpipufr hiupiuphpiulpuQiupjiuQ hpuGiunpmjpp 
umiugpG uliqpmQpp (inau Giuli 1.3 aGpiupiudpGp), QnijQiqhu luhinp t IpGbp GmjG $niGlpjpiuG, l}iujuilui& lipiujG pGtipgpiUL 
hiuuiulpupqtipp ppiup Glpuiniiiuup niGagiud hiuuiuupuuiiuupiiuG hiupiupapiulpuG uipiuqnipjniGGappg: Piujg, piuGp np 
upjiulpujpp upupiuqiujnui, puui uiuhuiuGuiuG, uijG Ipiipiipufr jt hiupiupapiulpuG uipiuqnipjniGGappg, iujl uijn $pqplpulpuG 
uh&nipjniGp* upjiulpujpp, Ipupiipufr t iSpiujQ upuimuhiupGDpp diuuiuGiulpiiiniupiufriujpG luniuGgpiupUJjppg, htunUuipuip 
upjiulpujpp pnpip yipu b , b , b U b uQfrnipjniGGQpp iqhuip t ipGbG ppuip hiuqMjJuiup: UjupGpG hplpu IpuiiiujiulpuG 
upuimuhiupGDpp upjL Qrpufr diuuiuGiulpuiniupiufriujpG hQniuipipnipjniGp pnpip pGhpgpiUL hiuuiulpupqhpniu (niqpn ph 
hiuqiuqpp) hiuuiniuinniG uQdnipjniG t, npp uhGp l}Q2UiQiuqhQp iSpiujQ «ti»-ni4 U uijG uiupQuiuinplpiphG IpupiniuhiujinUJi 
lujuiutm. 



b = b = b = b = b 



lljuiqpuni[ hplpu upuiniuhiupQhpp lipjU hrpu& uhgiulpxijpp, hiuuiudiujQ (1.9 - 13 )-nL[ U (1.9 - 14)-ntl mpOjUift piuGiudhhpp, 
pnpip ninjui h hiulpunhp fiGhpgpiUL hiuuiulpupqhpniu IpuGhGiu hhinhjiUL puiniulpuuuijpG inhupp. 



b 2 = Fx + A~x ~x + B~x = Fx + A~xq~x + B~x = Fx~ a + Ax~ a x~ + Bx~ = Fx~ a + Ax ox + Bx~ > 



1.9-15 



1.9-16 



(1.9 - 16)-ni[ inpipufr iSpjiuqiujpp lupimuhuijuimpjniQpg luniuGdQiugGhGp hhinhjiUL lunGynpjniGp. 

b 2 = fxl + Aio-t + B'x 1 = Fxl + At t + Bx 2 > 1.9-17 

(1.9 - 17)-p lihg uihrpuqphpiq' Cxo,x~} huil}iuiipp uinuiQgpuip0 1 hpp uipinuihuijinnipjnLQQhpp (1.9 - 12)-pg U quiimuphpii[ 
qripdnrpupjiuGGtip, pQjiqhu QiuU ppuip huiOjUiuuiphgCitipi^ (~x~ a J-p, f?o?Vp U (it J-p qnp&uil}pgQhpp, lihQp liuimuQiuQp A 
uiQhuijui qnp&uiljgp uipdhpp. 



\A = Fs\ 1.9-18 



llj QnihhinU (1.9 - 2)-nU [ U (1.9 - 3)^4 mp^uift 4,iujl}iuqujQ nu]pq dUiuq^npampjuiQ himluiuuipnuiGhpp iShj qppuinhpii[ 
(1.9 - 6)-ni[ U (1.9 - 7)-ni[ inpi[ui& hpqm upuiniuhiupQhpp iuniuQgpiupi[tipp, pQjiqhu QiuU qppuinhpii[ (1.9 - 10)-ni[ U 
(1.9 - ll)-ni[ inpi[ui& iSpUQnijQ hpqm upuiniuhuipGbpp uiniuQgpuipi[tipp uiuipphpnipjniQQtipp, iShQp l}uiniuQiuQp uiUjujl 
iquiuiuihuipQhpp lunuiQgpujpq'tipp iniupphpnipjuiQ mqpq dUunpnJunipjnLQQhpp, mripri U hujl}uiiipp pQhpgpunhuiiiuil}iupqhpniii. 

♦ UJiuijG mqfiq pGbpg/iwi huiiSwbwpqbpp rffipb 

= ^o-?'io = r(7)[(i + *|-)(i?2o-J?io) + *|-(j?2-i?i)] = r(7)[(i + *|-)?o + *|-j?] 
= ?2-?i = y(y~)\ (* 2 -^0 - -f(^2o -?io) = r(j){y- -F*oJ 

♦ UJiwjG hiubuiq/ip JiGbpgJiwi hwiSwbwpqbp[i uppb 

7 o = ^20-^10 = / 00 (^2()-?io) -g-c~Q*2 -^i) = y(y){yo- g-r**) 

^ = ^- < F' 1 -/(7)[(i + 4)(? 2 -V l ) + l(-2o-? 10 )]-r(v)[(i + 4)v + fv„] 

X>i3uiQuiiqhu (1.9 - 4)-ni[ U (1.9 - 5)-ni[ inpi[ui& ^iujquil}iuQ dUunpnJunipjuiQ hiuOjUiuuipnHSQlipp lihj ^ppiunhpiq' 
(1.9 - 6)-ni[ U (1.9 - 7)-ni[ inpi[ui& hpqm upuiniuhiupQhpp uiniuQgpiupilhpp, pQjiqhu QiuU ljppiuntipii[ (1.9 - 10)-ni[ U 
(1.9 - ll)-ni[ uipi[iu& upUQnijQ hpljni upuuiiuhiupQhpp iuniuQgpiupi[Qpp miupphpnipjniQQtipp, ubQp l}uuuuQiuQp uiOjun 
upuuiiuhiupQapp iuniuQgpiup4 D PP uiiupphpmpjiuQ hhuiUjun dliiuipnJumpjiuQ hiuqMjjuiupnuSGapp. 



42-82 



1.9-19 



1.9-20 



Upuj^uiip Injhpp ^uipuiphpiulpuG CuipdiiuiG ShumpjniQ 



♦ 4wljiuqpp L mqpq pGhpgpwi hwitwliiupqhpfi itpph 



x = 7 






1.9-21 



♦ fliilM li hwljiuppp pGhpgpwi hwiSwljwpqhpp iSpph 



?' = -r(v)[(i + 4)*+l*o] 



1.9-22 



t'ul} uijdiS (1.9 - 16)-ni[ inpipufr iSpjuilpjijpp wpuiuihuijuinipjniQpg uinuiQdGuigGtiQp hauiUjuiL uinGyiipjiuGp. 

b 2 = Fx a + A~x a ~x + Ex = Fx + A~xa~x + Ex > 

(1.9 - 19)-ni[ inpipufr (~Xa,lc J uinuiGgpuipilhpt 1 AUimJinJunipjuiQ uipuiuihuijuinipjniGGapp uihrpuqptipiq' (1.9 - 23)-p iShj 

U uuiuigipud himpiiuuipiiuiG iSh$> ppiup hiuipuuiupagGauiil f ? () J-p, (?o?Vp U f ? J-p qnp&iuljpgGhpp, pGjiqhu GiuU iujq 

qnpfriuljpg Ghpp qphpii[ puui v hiupiupupiulpjiG uipiuqnipjiuG luuuipiSiuQiugmjgp uiiMiuG, iSuGp IpnniuGiuGp liQinLjiUL 
hiuiliuuiupnuJGapp hiuiSiulpjjpqp. 



< 



1) Y 2 (y) F+{2Fs-A)^ + (Fs 2 -As + B)^- 



2) y 2 (lT) 



= F 



A + (2Fg+As - 2B)-£- + (2F.v - A)g-^- 

c 

3) y 2(^)^ + Air|- + F^^-^= B 
(1.9 - 24)-ni[ iSh$> inhrpuiipaniil (1.9 - 18)-ni[ inpipiifr A qnp&iuljgp uipdhpp, iSuGp IpiiniuGiuGp. 

1) y 2 (v)(V + Fs^-+B^- i - / 



2) 7 2 (v) 



Fs + (2Fg + Fs 2 - 25) -£- + Fsg-^- 



= Fy 



3) y 2 (v)(B + F S g-^-+Fg 2 



B 



UjQnihhinU ppiup i)piu piudiuGhpiil (1.9 - 25)-nil uip4iu& hiuipuuiupiuiSGapp huniiulpjapqp IpxuSiujiulpiiG aplpu 
hiuiliuuiupnuiGtipp U papopiil iujG pGnhiuGmp hiujiniupiupp, pG^iuhu QuiU ppiup hun[iuuiupbg Qbpii[ v hiupiupapiulpuG 
lupiuqiupjiuG GmjG uimnpiSiuGiugnijgp qnp&iuljpgGapp, lihGp IpiuiiuGiuGp B uidhuijui qnp&iuljgp uipdapp. 



B = Fg 



(1.9 - 26)-ni[ npr^ipufr B qnp&iuljgp uipdhpp uiarpuqpapiil (1.9 - 25)-i[ inpipufr hiuiliuuiupnuiGtipp hiuiSiulpjjpqp npUt 
hiuiliuuiupiiiuG iSq$>, lihGp IpiuiuiGiuGp 7 2 (^) qnptniUjgp uipiniuhiujimupjiuGp. 



y*00 



> 



1+5^+^ 

c c 

(1.9 - 27)-ni[ npr^ipufr 7 2 (^)-p lupuiiuhuijuinipjniGp uianiuqpQpiil (1.8 - 21)-ni[ uipihu& d(~vj nprypjp 
uipiniuhiujimupjiuG lihg, pG^iuhu GiuL ilaphfytiniil (1.8 - 20)-p, iShGp IpnniuGiuGp. 



rf(V) = tf("v) = 1 



(1.9 - 28)-p lippiunhpiil (1.8 - 21)-p hplipnpij hiuiliuuiupiiiuG iSq$> iShGp IpnniuGuiQp y 2 (V Vp lupuiiuhiujuimpjiuGp. 



y 2 (V) = 



> 



-jr+g- 



1.9-23 



1.9-24 



1.9-25 



1.9-26 



1.9-27 



1.9-28 



1.9-29 



43-82 



4,uijlpxiquiQ -iuipuiphpuilpuQnipjuiQ ^unnnilj ShunipjniQ 



f»ul}, huiiiui&uijQ (1.3 - 1 1)-Ji, puiQp np y qnp&uiljpgQQpp iqtunp t ihQhQ qpuilpxiQ lih&mpjniQ, hQuiLuipuip (1.9 - 27)-pg 
U (1.9 - 29)-pg iShQp qMjpjQuiquiQuiiqDu y qnpdui qpg Q Dpp hunSuip quuiuiQuiQp htunujuqpuiQuKiuQpp. 




lIjQmhtunL (1.9 - 28)-niJ uipqMn& npn2pjQhpp uipdhpGhpp uiDquiqpQpiq' (1.8 - 22)-p iShj, QhQp quuiuiQuiQp htunujuq 
uinQyiipjniQQtipp, npnQp (Sp2Ui bQ IpxnSuijuilpuQ v U v niqjiq U huilpuiipp huipuiphpuilpiiQ uipuiqnipjuiQ quid 2uipdU 1 nq 
q*inp6Qujl}uiQ iiuiuQpl}p 1}uhSuijuiI}uiQ w mqpq U hiul}uiqpp uipuiqnipjniQQhpp hiuiiiup. 



r(w) = r(w) (i + .s'f) = /j(^)>o 

y(^) = r (V)(l+.s|Q=/?(V) >0 



£uiQp np, huiiiuifiuijQ (1.3 - ll)-p, y qnp&uiljpgQQpp iqtunp t ihQhQ qpuilpuQ lih&mpjniQ, hQinUuipuip (1.9 - 27)-pg, 
(1.9 - 29)-pg U (1.9 - 31)-pg hhinUniiS t np IpuiSuijuilpuQ w niqjiq U huil}uiqpp uipuiqnipjniQQQpp huniuip uihqp mQhQ 
htunUjuq uinQyiipjniQQtipp. 




X>mjQu}hu (1.9 - 28)^4 uipqMn& npn2pjQhpp uipdhpQtipp uiDquiqpQpiq' (1.8 - 23)-Ji iSq$>, lihQp quuiuiQuiQp htunujuq 
umQynpjniQp, npp QnLjQiqtiu (Sp2in t IpuiSuijuilpiiQ huipuiphpuiquiQ uipuiqnipjuiQ Ijuiil 2uin cn l nr l ihnpdQuiljuiQ QuiuQplip 
quiuuijuiquiQ uipuiqnipjuiQ huniuip. 



yfwjw = —y(wp 



1.9-30 



1.9-31 



1.9-32 



1.9-33 



Cun.q&nui 1 -22 - hpb (1.9 - 19)-ni[ mpUwd f 3? , 3? J ninfin wnwGgpwpilhpp. dbwUinpjmpjLuG hiuUiuuiupniiiGbpp 

UmpjmpbG oqwwqnpdbGp (1.9 - 20) -ni/ bwif (1.9 - 21) -nil b tjuiif fy (1.9 - 22) -nti wptiuid LumuGgpwpUbpp dbwUinpjmpjwG 
hwilwmiipmiSGhpp b qpwGp whqwripbGp (1.9 - 16) -ni] inpdiud iSIigwbwjpp. hwGwuiiuinwupjwG wnG^mpjuiG iShp, uiujui iSbGp 
GmjGujbu bumwGiuGp (1.9 - 30) -ni[ mpGuifr pwGwdbbpp: 

(1.9 - 18)-n4 0- (1.9 - 26)-n4 inpihufr A Q B qnp&mqpgQhpp uipdhpQhpp uihquiqpbpiq' (1.9 - 16)^4 inp^iuft iipguil}uijpp 
uipinuihuijinnipjuiQ dhg, iShQp lijijuilpiijpli puinuilpuuni huniuip IpnnuiQuiQp hhinUjuq puiQuidLp. 



b — r[x + sx x + gx J — r[x Q + sxox + gx j = r [ Xq + sx x + gx 1 = r ( Xq + SXoX + gx \ > 



(1.9 - 34)-ni[ inpihufr iSpjuiquijpp puinuilpuuni puiQuidUhpp qpq^uid qp^hphQgpuqQhpp inhupni[, InjiQhQ. 



r db 1 -- 


- F[ dx + sdx dx + gdx J = 


= fI dx + sdxodx + gdx ) > 


I db 1 -■ 


= F[ cfx t ) + sctx ctx + gdx J = 


= F[ cfx + scfxQttx + gctx ) > 



1.9-34 



1.9-35 



Ujdii hQpuiqphQp, np P qhnp6Quil}uiQ iiuiuQfil}p K' mqpq U huiljuinpp pQbpgpuq huniuil}uipqtipp Ql}uiuiiiunip 2uipdq , miS t 
hunSuiu}uiinuiuJuuiQuipuip u U u uipuiqnipjniQQhpn^, pulj QmjQ dinpdQuiqujQ iSuiuQpqp K mnjiq U huiqujqlip pQhpgpuq 
hunSuiquipqhpp QquuniSunSp 2uipd4mii t huniuiuiuiuiuiupiuiQuipuip w U w uipuiqnipjniQQtipnq': Uj QnihhuiU 4bphji2bnnl 
(1.8 - 3)-ni[ U (1.8 - 4)-ni[ uuihiiuiQq'ui& mqfiq U huil}iuqpp uipuiqnipjniQQhpp puiQuidUhpp, pQjujliu QuiU (1.9 - l)-ni[ uipi[ui& 
Q2UiQuil}miiQhpp U Ijppuintqnq' qpuiQp (1.9 - 34)-p U (1.9 - 35)-p lihg, dpnpdQuiljuiQ iiuiuQlil}p hunipQpuig l}unS quiiiuijuiquiQ 
uipuiqnipjniQQtipnq^ 2uipdiSuiQ qtuqpmii QhQp iSJijuiquijpti puinuiqmuni U qpui qp^hphQgpuiiJi hunSuip quinuiQuiQp htunUjuq 
uipinuihuijinnipjniQQQpp. 



44-82 



Upui^uup Injhpp ^uipuiphpuiquiQ CuipduuiQ ShumpjiuQ 



♦ <PnpdGwl]wG iSwuGphp hwiSpGpwg 2Ujpdi!iuG pbujpmii 



ti 1 = F \\+sSr + 



«W"< 



b 2 = F 1 + ! a + jJL. u c ; =F , 1+s x. + g 



c C 



„ W i .. W 



> 



(cVV > 



1.9-36 



♦ 0npdGwl]iuG UwuGphp l]iuiSwjwl]iuG 2wpddwG qhuipmiS 



dti 1 = F 



J/z 2 = f(\ + s%- + g-^-Vc<*VY ^Ffl+^+g^VcY/V) 2 > 



1.9-37 



£uiQp np, huiuuiduijQ (pQqqdiuu 1-10)-p, (1.9 - 27)-nil U (1.9 - 29)-nil inpipufr puiQuidlihpp 6p2in hQ QuiL IpuiSuijuilpxiQ 
uipuiqmpjuiQ (mqpq IpuiS huiquiqpp) huiiiuip, hQinLuipuip (1.9 - 36)-nil inpipufr puiQuidLp uq$> huupuuuipuuiQ uiuhQuiduitu 
IpiqiSp* {ti 1 ), qpuiquiQ iSh&mpjniQ t, pul} uig Ipirpip prqnp uipinuiqpp^Qtipp, puiguinmpjuiup F qnp&uiljgpg, QnijQiqhu qpuiquiQ 
i5h&nipjmQQhp hQ U hhinUuipuip qpuil}iu(i lih&mpjmQ iqhinp t iJiQp QiuU F qnp&uiljpgp: Puigp qpuiQpg, puiQp np F 
qnpfruiqpgp nj lip qhp jp quiuiuipnuS upjuiquijpp puinuilpuum puiQuidlihpp uq$>, lihQp uinuiQg pQqhuiQpiupjiuQp IpipgOhnu, 
quipnq hQp uiqiuinq'tn qpuiGpg pQrpuGQuiqV 

F = +l 1.9-38 

F-p uipdhpp (1.9 - 38)-pg inhqiuqphpiil (1.9 - 34)-nil inpipufr upjuiquijpp puinuilpuum puiQuidLp uuj, pQjiqhu QuiU 
oqiniltimil (1.9- l)-p Q2UiGuilpuuGQppg, uhGp L[hpgQujLitu(iuiLLihu ImuiuiGuiGp. 



ti 1 = lc~t ] +slc~t \x + gx = (c~t) +s(c~tpt + g5? = (ct ) + s(c7 yx + g*x = (ctj + s(ctyx + g*x > 



f'uli (1.9 - 39)-nil inpipufr iSpjiuquijpp puinuilpuum qp^hphQgpuqQhpp huuSuip uhGp IpunuiGuiGp. 



dti 1 = (cdf} + s(cd~t'\(dx'^ +g(dx'y = (cdtY + s(cd~t S \(dx s ) + g^dx) 2 > 
dti 1 = (cXi^j + s(cd*t'\(ttx''} + g(dx'Y = f cdY) + s (cd*t Vdx ) + g(rf*) 2 > 



X>mjQu}hu F-p uipdhpp (1.9 - 38)-pg inhnuinntimil (1.9 - 36)-ml U (1.9 - 37)-ml inpipud uipinuihuijinmpjmGGQpp lihg, 
pQ^iqhu QuiU 1 hphp2Qpiq' (1.9 - 27)-p U (1.9 - 29)-p, uhGp upjuilpujpp U pp qp^IphptiGgpuiip huiiiuip ImuiuiGuiGp QuiU 
hhinlijun puiQuidUtipp. 

♦ 0npdGwl]iuG UwuGphp hwiSpGpwg 2uipdiSwG pbujpmii 





* = Ji + 4 + *£ ( c/ ) - J 1 + 4 + ^ ( c7> ) - J 1 + 4 + *^r ( cV ') - J 1 + 4 + ^ (^) > o 






♦ 0npdGwhwG itwuGphp IpuiSwjwhwG /ujpdii'iuG qhuipmiS 




db= j l+ 4 + g ^L ^r') = Ji + 4 + g^j- (cdt) = ji + sf + g^j- (cdY) = ji + 4 + g ^ (^r) > o 



1.9-39 



1.9-40 



1.9-41 



1.9-42 



45-82 



4,uijlpxilpiiQ <uipiuphpuil}iuQnipjuiQ ^imnnilj ShunipjniQ 



1.10 - Puiguipduilj cfuiiJuiQuil[]i U Puiguip&uili lIjiuiqnipjuiG UuihiSuiGmiSp 
U Puiguip&uiq UpuiqnipjuiG £)Luii|infunipjuiG -^uii|uiuuipniGGbpp 

chjjiiuiGuiqp lip pinphprpu^np $pqplpiilpuG hpUnijp t, npp uinuiplpiijujlpiill piipnGnuip 2uiui IpupLnp t J^IPP 111 
IppqplpulpiiQ uihumpjniQ Ipunmghpu hunSiup: f!puiu[Qu, duuiuiQiuqp hiuulpugnrpupjuiQ liiuupQ piiuiuiniuuppiulpuG U 
qhGuuipuiGuilpiiG unuibgnuSGopp hhGg 20-pq rpupp uljqppG ipnpiuippGilhgpG uiilhlP 2 mm duiiluiduilip pGmjpp $pqplpiilpuG U 
puiGuilpulpiiG hhinujqnimSuuSp , npp mrppulip lupryniGgp hiuGiipuuiguiG dmuuiQiulpuuiuipuj&nipjujG huiinmAj 
hiupiuphpuilpiiGnipjuiG U pGnhuiGnip huipuiphpuilpuGnLpjuiG uihunipjniGGhpp uuihnfrmiip: 

Uju puidGnuS iSUGp IpnuhiSiuGhGp U qpGGuipqhGp ipqplpujp huiiiuip 2uiui IpupLnp* pwgwpdwb dwiSwGwbp 
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hunSiup Uu lihGp quiuhiiuiGtiGp pphQg himSiupdhp puiguipdiuq lih&mpjmQQhpp: 



UuihiliuQnuI 1-4 - £wGp np, hwiSwdwjG (1.9 - 39) -p., bpqm wwwwhwpGhpp iSpph bqw& iSppuibwjpp pwnwbmu/iG, 

pnpip pGbpgpwi hwiSwliwpqbpmiS (mqpq pb hwl]wq[ip) hwuinwinniG iShdnipjmG t, hbmbwpwp wjq ipwump Ubq hm^niU t np 
dbGp l/wpnq bGp uwhiSwGbi pwgwpdwli dwrfwGwl][i hwubwgnqmpjniGp, npp qmGbGw GmjG iSbdmpjmGp pn[np fiGbpg/iwi 
hwtSwbwpqbpniU (mq[iq pb hwhmqpp), L wjG UbGp qG^wGwbbGp T -ni[: Ujuwjiund pwgwpdwli dwUwGwqp L pp 
q[ij>$>hphGgpwip dbGp huwhiiwGbGp hbwhjwi qbpw. 




1.10-1 



Oquiq'hpiq' (1.9 - 39)-nU [ U (1.9 - 40)^4 uipdjuft piuGuidLtippg U (1. 10 - l)-ni[ inpipiifr G2iuGuilpuiiGDppg, piuguipdiuq 
duiuuiGuiljp puiniulpuum U lyiui njiIp^pDpDGgpuqp hunSiup iShGp IpnniuGujGp hhinLjiUL uipinuihuijinnipjniQQhpp. 



♦ K U K mqfiq JiGbpgfiwi hwiSwbwpqhpmiS 



1 



b 2 = ? + s4-? it + g 



t +.v-jr t x +j-ji > 



dr 2 = -\rdb 2 = d~t + s^rdt d~x + g-^rdx' 1 = d~t + s\d~td~x + g-^dx 2 



1.10-2 



♦ K b K hwl/wqfip pGbpg/iw[ hwiSwqwpqbpmiS 



■b 2 = 7 + s\-*i'x + g- 



1 V' 2 



1 V 2 



SJrtX +J-jI > 



dx 2 = Ardb 2 = d*t + s\rd*t <fx + gArdjc' 2 = it + s\rd*t<fx + gArdjc 2 



1.10-3 



f>uli q^npdQujlpuli liuiuQplip huiiipQpuig l}unS quiiiuijuiliuiQ uipuiqmpjunSp 2UjpdiSui(i qtnqptipp huiiiuip oquii[tiinq' 
(1.9 - 41)-ni[ U (1.9 - 42)-ni[ inpi[iu& piuQiudUhppg, iSbQp piuguipduil} dunSuiQuil}p U pp ijp^hphQgpuiiJi hunSiup quimuQuiQp 
hhinlijun ujpinuihiujinnipjniQQhpp. 



♦ 0npdGwbwG iSwuG/ibp hwiSpGpwg 2wpdi!wG qbwpnid 





r = |*=v'Ji + 4 + ^ =rJi + 4 + *|i =rJi + 4 + «^ =?Ji + 4 + ^ > 




♦ 


0npdGwbwG UwuGJibfi bwiSwjwbwG 2wpddwG qbwpmiS 




dx - ±db = ji + 4 + g £. ( rf r') = ji + 4 + gt, (dt) = ji + 4 + g^- (A) = Ji + 4 + ^ (rf?) 



1.10-4 



1.10-5 



46-82 



Upuj^uiip Injhpp ^uipuiphpiulpiiG CuipdiiuiG ShumpjniQ 



Uj QiuhtunL oquiuiqnp&hpiil (1.9 - 30)-ni[ npn2ipiifr J qnp&uiljpgGhpp piuQiudliQpp u U w mnpq U huilpuqpp 
uipuiqmpjniQQtipp huniuip U uihquiqpQpiq' qpuiGp (1. 10 - 5)-p iSq$>, lihQp quuiuiGuiGp piugiupduil} U inhnuilpjjG diuiSuiGuiljp 
qpIp^tiptiGgpuqGtipp iSpjU hrpxid htunhjuiL uinGyupjiuGGtipp. 

1 J7 — 1 a? - 1 J7 - L 



dx 



-dt 



-dt 



-dt 



-dt 



y(u) y(u) r(w) y(w) 

(1.10- 6)-ni[ inpipufr hiui[iuuiupniiipg lihQp Ipupnq hGp uiniuGuiL GuiL hhuiUjuq uinQ^nipjniQQhpp. 



dt 
dx 



dt 
dx 



*k ~ 'CO 
dt 



XiiSuiGunqhu (1. 10 - 6)-pg quid (1.10 - 7)-pg lihQp Ipupnq hGp uinuiGuiL GuiU hhuiUjuq uinQ^nipjniQQhpp. 

it _ y(") f A. = y (^) 

it _ y(") I ji? = K"0 

rf? y(w) d / r(«) 



1.10-6 



1.10-7 



1.10-8 



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pnpip [lGbpgfiwi hwGwbwpqbpmG (niqpq pb hwbwqfipj, uiujiu wGhpwdb^m t np G/iGjb wjdG Gbp oqwwqnp&wd t' b t 
dwGwGwbp uiwppbpbGp Gnp GhpGmddwfr pwgwpdwb dwGwGwGJig b qpw hwiSwp, wjumhbmb, GbGp wjG bwGGwGbGp 
mbqwbwG dwGwGwb: bi fiGjiqbu wpnhG GbGp q/imbGp, mbqwbwG dwGwGwbp mwppbp t nj GfiwjG ppwp GbwmGwGp 
hwpwphpiubwG 2iupdiSwG Gbp qmGdnq fiGbpgfiwi hwGwbwpqbpniG, uij[ wjG miuppbp t Gwb mwpwdmpjwG hwjbpujpG 
wGqpwqwpdGwd JiGbpgfiwi hwiSiubwpqbpmiS, pGjp GbGp GwGpwGwuG jwpwqpbi bGp (1.8) pwdGniG: 

bplpu inhuiuqp chmSuiQuiljGhpp qnjmpjuiQ ipiuuuipg hhuiLnui t np iqhuip t qnjmpjniG iuGqGuiG QujU hplpu inhuiuqp 
lupiuqnipjniGGhp, lupiuqiugnuSGhp U pGnluuGpiuiqhu iqhuip t qnjmpjniG niGhGiuQ hplpu uihuiuljh diuiiuiQuiqpg 1}uiJu4uj& 
5>pqplpjjlpu(i lih&mpjniQQhp 1 inhqiulpuG U puigiupdiuq: ^hinhiupiup <iujlpulpiiG hiupiuphpiulpiiGnipjiuG hiuuiniq uihumpjiuG 
i5h$> 2UJin qiuphnp t uuupphpiuU_tq U huiniuq uiuhiSiuGtq inhqiulpud U piugiupduilj IjipqplpiiqiuG iShdmpjniGQhpp: Ujq 
Qiqiuuiiulpiq' giuQlpugiu& puiguipdiulj Ippqpqiulpxill lih&mpjuiQ hiuiSiup iShQp Ijoquiiuqnp&hGp «p» uinnppQ gmgp^, npiqhuqp 
inuippQpuiqtiGp piugiupduiq $pqpl}iuqujQ iSh&nipjmQQhpp hunSiuiquiuiujuJuuiQ uihquiljuiQ 4)pqpl}iuquiQ iSh&nipjmQQhppg: 

UaihdiuQnuI 1 -5 - &np6GwbwG GwuGpbfi wGgwd tiwGuiupuphp. jiuifip pum G/iwdnp inbqiubwG diuGuiGwhJi GbGp 
GmGdiuGbGp inbqiubwG wpwqnipjmG, Jiuh ifinpdGwGiuG GwuGp.GJi uiGgiud duiGwupuphp. jujGip pum GfiuiGnp pwgwpdwu 
dwdwGwbp. GbGp GwGGujGbGp pwgwpdiub wpwqmpjmG: XrduiGwiqbu GbGp Giupnq bGp uwhGwGbi Gwb inbqiubwG b 
pwgwpdwb wpwqwgmGGbpp: ■(hwbwpwp, GinpdGwbwG GwuGfibp. npwbwwbu Jipwpjig mwppbp wju bpuni 
wpwqnipjmGGbpp b wpwqwgmGGbpp K' b K niqjiq b hwbwqfip JiGbpgJiwi hwdwuwpqbpniG GbGp Gwpnq bGp uwhGwGb{ b 
G^wGwl]b[ hbmbjwi bbpw. 



< 



♦ K b K niqfiq ]iGbpgJiwi hwGwuwpqbpniG 

SbqwbwG bwG "bjmmnGjwG wpwqnipjmG 

SbqwbwG bwG "bjmmnGjwG wpwqwgmG 

fiwgwpdwb wpwqnipjmG 
fiwgwpdwb wpwqwgmG 



dx 

dt 

du 

dt 

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dx 

du ? 
dx 



dx 

d~t 

dw 

d~t 

. dx 
dx 

dw f 
dx 



1.10-9 



47-82 



^.lujlpulpiiu -iuipiupupiulpuunipjiuG ^uiinnilj StiunipjniQ 



♦ K h K hwbwqpp fiGhpgfiwi hwiiwbwpqhpmii 
SbqwbwG bwd "bjmmnGjwG wpwqnipjmG 
SbqwbwG bwii "bjmmnGjwG wpwqwgmiS 

fiwgwpdwb wpwqnipjmG 
fiwgwpdwb wpwqwgmiS 



u = &j 
dt 

t _ ctu 

ctt 

tr = &- 

Uf ~ dx 

aup 

~dT 



bo = 



ctx 

ctt 

dw 

ctt 

. ctx 
dx 

dw n 
dx 



1.10-10 



UjunihQinL piugiupdiulj diuiSiuuiuljp dx qp^pIpopQugpiuip lupuiiuhiujuinipjniup (1. 10 - 6)-pg uitiniuqpQpiil (1. 10 - 9)-p U 
(1. 10 - 10)-p lihg, pQ^ujtiu QiuU oqim[bpiLl uihniulpxiu lupiuqnipjniuuhpp (1.8 - 3)-ni[ U (1.8 - 4)-ni[ inpipufr uiuhiiiuGnuiutippg, 
iShQp IpiinuiQiuup piugiupduil} uipuiqmpjuiQ U inhrpulpuG lupiuqmpjiuu lipgU hniu& Ipuiqp K' U K mqpq U hiulpuiipp 
pQhpgpun huniiulpxipqGpnui. 



K U K pQhpgpuiL hiuiSiulpjipqapniiS 

«— — * 

K U K puhpgpiUL himSuilpjipqhpnuS 



Up = yfuju 
w f — yfwjw 



u P = yfuju 
w P = y(wjw 



1.10-11 



UaihiliuQnuI 1-6 - (1. 10 - 9)-nd, (1. 10 - l0)-ni/ uwhGwGGwd U (1. 10- \\)-ni/ wpi/w& pwgwpdwb wpwqnipjmGGhpp 

ppwbwGmil hwGqpuwGmil hG pwgwpdwb wpwqmpjwG mwpw&wuwG pwqwqppjGbp: ■Cbwhwpwp, (1. 10 - W)-pG 
hwiiwGdwG, libGp bwpnq bGp uwhiSwGbi GwL ipnpdGwbwG rfwuGpbp pwgwpdwb wpwqnipjwG pdwjpG pwqwqppjGbpp K' I 
K mqpq h hwbwqfip pGbpgpwi hwdwbwpqbpmil ' hbwbjw[ bbpw. 



dXn /<-\ 

cfxp 
dx 



dXn /->\ 

dxp 
dx 



K U K puhpgpiUL himSuilpjjpqhpnuS - ( 

K U K pQhpgpuJL hiuiSiulpiipqapnuS - w p = — j^- = y(w~)c U w p = - = y(w~)c 

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pwqwqppjGbpp K L K' pGbpgpwi hwrfwbwpqbpp hwiiwp hbwbjwi bbpw. 

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GbwwiSwiSp 




♦ K pGbpgpwi hwiSwbwpqp ^wpdiSwG pwgwpdwb wpwqnipjwG pwqwqppjGbpp K pGbpgpwi hwiSwbwpqp 
GbwimiwiSp 




1.10-12 



1.10-13 



1.10-14 



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uipuiqnipjiuQ puu\iuri : pp^Qhpp hhui: 



♦ K b K pGbpgpwi hwdwbwpqbpp rfpgb 



r ^o 


-»° , -» 




r ->o 


<-<) , <- 


u„ - 


= Mp + SUp 




u„ - 


= Up + SUp 


< p 


UuiiJ 


1 




— > 




-» 




[ «p = 


- -Up 




[_ «p = 


- -Up 



1.10-15 



48-82 



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♦ K b K pGbpgpwi huiiSuibiupqhpp iSppb 



f s-° 


— >0 




r _* 


<— 


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= W p + iWp 




w„ 


= Wp + iWp 


\ J- 


IpuiJ 


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= -Wp 




[_ VVp 


= -Wp 



1.10-16 



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f° > 

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y(w)r(w') = 1-g- 



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1.10-17 



1.10-18 



1.10-19 



1.10-20 



1.10-21 



1.10-22 



49-82 



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= yfwjw = 



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1.10-23 



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(1. 10 - 16)-/z, GGmii t GmjGp: 



bi L[b.pguiujhu, quiiSuijuiquiQ w uihquiquiQ uipuiqnipjuiQ huiiSuip, QmjQujhu oqinqMimq' (1.9 - 27)-ni[ U (1.9 — 29)-ni[ 
inpi[ui& y qnpduiljgp puinuilpuum puiQuidLhppg, pQ^uphu QuiL oqinqMamq 1 (1. 10 - 1 1 )-ni4 U (1. 10 - 12)-n4 uipq\u& puiguipduiq 
uipuiqmpjuiQ uiuipui&uiquiQ U pqMujpQ puiruunpp^Gbph uuihiSuiQmu'pg, lihQp IpjuiuiQuiQp lip qhqhghlj puiQuidh, huiiSuiduijQ npp, 
luuiiuijuilpuQ puiguipdiuq uipuiqmpjuiQ pipiijpQ u inuipui&uilpuQ puiquiqppjGbpp, mqpq h huilpuqhp hQhpgpuq 
huiiSuilpupqhpmu', puuluipuipnui hQ hhuihjuq uinQyupjuiQp. 



W 



+ sw p Wp + g 



(w P ) 2 = (w°) 



+ SWpWp + g 



(w P ) 2 



1.10-24 



I^ub. (1.8-33)-piSbg l}hpuinhmi[ (1.10- ll)-ni[ (1.10- 12)-nq\ (1.10- 13)-mlh (1.10- 14)-ml uuihuuiQqui& puiguipdiuq 
uipuiqmpjmQQhpp pq\ujpQ h uiuipui&uib,uiQ puiquiqpp^Qhpp uipuiuihuijuimpjmQQhpp, iShQp IpiinuiQuiQp puiguipdiuq 
uipuiqmpjmQQhpp uiiupphpmpjuiQ pihujpQ u inuipuifruilpuQ puiquiqppjQhpp dhuiQinhimpjuiQ huuluiuuipnuiQhpp. 



"p = "f(/p w p -SVfWfJ 

T? P = -i- f V pWp + Wp V P + .sVpWp J 



<_o J ^->o<_o _> <_ \ 
»p = -^(^VpWp - gv r w f J 

<- 1 /^->"<- 



1.10-25 



X,uuiQuuqhu (1.8-34)-puhg l}ppuinhmi[ (1.10- ll)-ni[ (1.10- 12)-nq\ (1.10- 13)-mlh (1.10- 14)-ml uuihuuiQqui& 
puiguipdiuq uipuiqmpjmQQhpp pihujpQ h inuipuifruilpuQ puiqiuqppjQhpp uipinuihuijinmpjmQQhpp, lihQp ImuiuiQuiQp 
puiguipduili uipuiqmpjmQQhpp qmiiuipp pq\ujpQ U uiuipui&uiquiQ puiquiqpp^Qhpp dhuiipnhimpjuiQ huiqMnuuipmiiQhpp. 



Wp = — (^Vp«p -gv f u v J 

Wp = -i- f "v p T?p + T? p "i?p + .?"? p 7?p J 



w p = t(, v p"p _ £ v p m pJ 

Wp = -i- ( V~ p W~p + t7pV p + 5 



1.10-26 



UjQmhhinh (1. 10 - 25)-ni[ U (1. 10 - 26)-ni[ uipijuift mqpq h huiquiqpp puiguipduili uipuiqmpjmQQhpp inuipphpmpjuiQ U 
qmiiuipp uiuipui&uilpiiQ puiquiqpp^Qhpp uipuiuihuijuinipjniliQtipp iSbj uihquiqphpii[ (1. 10 - 22)-ni[ uipi[ui& puiguipduili 
uipuiqnipjuiQ mqpq U huiljuiqpp pi[uijpQ puiquiqppjQtipp uipuiuihuijuinipjniQQhpp v, u V w uipuiqnLpjniQQhpp huuiuip, iShQp 
mqpq u huiljuiqpp puiguipduiq uipuiqmpjniQQhpp uiuipptmnipjuiG U qmiSuipp uiuipui&uiquiQ puiquiqpp^Qhpp huuiuip 
IjuuiuiQuiQp QuiU hhuiUjuq puiQuidUhpp. 



1 T?p = A(vp)wp - A(Wp)"?p 


U 


| t7 P = A(vp)wp - A(wp)Vp 


1 Wp = A(vp)T?p + A(wp)"vp 


1 Wp = A(vp)t7 P + A(w P )Vp 



1.10-27 



XiiSuiQuiuihu (1. 10 - 25)-ni[ U (1. 10 - 26)-ni[ uipi[ui& mqpq u huiquiqpp puiguipduiq uipuiqmpjmQQhpp uiuipphpmpjuiQ u 
qmiJuipp p4 m ltQ puiquiqpp^Qhpp uipuiuihuijuimpjmlilitipp iShj uihquiqptqnq' (1- 10 ~ 22)-nq' uipi[ui& puiguipduilj uipuiqnipjuiQ 
mqpq u huiquiqpp piJuJltQ puiquiqpp^Qhpp uipuiuihuijuimpjmQQhpp v, u U w uipuiqmpjmQQhpp huuiuip, pQjujhu Quih 
(1. 10 - 27)-m[ inpipiifr hunSuiu}uiuiuiuhiuiQ puiguipduiq uipuiqmpjmQQhpp uiuipui&uiquiQ puiquiqpp^Qhpp, lihQp IjuuiuiQuiQp A 
qnp&uiljpg Qhpp hhuiUjuq dhuiqhnhimpjuiQ puiQuidhhpp. 



A( Mp ) = A(v P )A(w P ) + (g- V)- 



A(wp) = A(vp)A( Mp )-(g-|.v 2 ) 



c 

VpMn 



1.10-28 



50-82 



U|iuj^uh}i Injhpp <uipuiphpiuquiG CuipchiuiG ShumpjniQ 



Ujdii npiqhuqp ^uijquilpiiG InupuiphpuilpjjQnLpjuiG huiuimq uihumpjuiG (1.8 - 25)-ni[ U (1.8 - 26)-ni[ inpi[ui& luqpq U 
hiuquiquipd dUuiipnpanipjuiQ hiudjuuiupnuiGhpp uipuiuihuijuihQp v P puiguipduili hiupiuphpuilpxiG uipuiqnipjuiiip, uiupu 
uiQhpuidb2Ui t np iSUGp v hiupiuphpuilpiiG uipuiqnipjuiG huiiSuip oqinqMiGp (1. 10 - 17)-ni[ U (1. 10 - 20)-ni[ inpi[ui& 
puiQuidlihppg, pG^iqhu GuiU oqim[bQp (1. 10 - 13 )-nL[ U (1. 10 - 14)^4 mp^uift piugiupduil} hiupiuphpuilpiiG uipiuqnipjujG 
puirpuqppjGhpp uiuhiiuiGnuipg: Ujuu[puni[ iSUGp IpnniuGuiGp ^uijlpulpuG huipuiphpiuquiGmpjiuG huiuiniq uihumpjuiG hhinLjuiL 
dUuiq^npanipjiuQ hiudjuuiupnuiGhpp. 



♦ 4wjqwl]wG dbwipnpjmpjwG hwGwuwpmilGbpp K L K mqpq pGbpgpwi hwiSwl/wpqbpp iSppb 



Htqpq dUuiqhnJunipjnLQQhp 


<uil}iuquipd dUiuq^nJunLpjniQQhp 




f 

7 = 


A(vp)+fv^ 


-» v, -> 
t +g—fx 




7 = 


A(Vp)-1^ 


7 -g-^f7' 


< 


x — 


A(v P )-i,^ 


x — v f t 


U < 


X = 


A(v P ) + i.vlL 


X + V p t 




< J 




V J 



1.10-29 



♦ 4wjl]wbwG dbwipnpjmpjwG hwUwuwpmiSGbpp K b K hwliwqpp pGbpgpw[ hwilwliwpqbpp iffipb 



fUqpq dUuiq^nJunLpjniQQhp 


^uilpiirpupd dUuiq^npanipjniQQtip 




t = 


A(v P )-fv^ 


<- V pf - 

t -g— r x 




r 
<— 
t = 


AM + fv^ 


<-' Vp <_' 

t + g-^x 


< 


x — 


A(v P )+fvi 


X + Vp t 


U < 


X = 


A(v P )-i^ 


X — Vp t 




< - 1 




L J 



1.10-30 



\>i5uiG dbm[ iSUGp Ipupnq hQp <iujquilpxiG huipuiphpiuquiGmpjiuG huiuiniq uihunipjujQ (1.8 - 27)-m[ U (1. 
inpdjufr dUiuq^npanipjiuQ hiudjuuiupnuiGhpp uipuiuihuijuitq v P puiguipduilj hiupiuphpuilpiiG uipuiqnipjuiiip: 



28)-n4 



♦ 4wjqwbwG dbwipnpjmpjwG hiuGwuwpmUGbpp K b K pGbpgpwi hwiSwbwpqbpp iSpgb 



2 C 



A(vp) 
A(vp)-|,^ 



i A(v P ) + (g-|.v 2 )- 



1.10-31ui 



♦ 4wjqwbwG dbwipnpjmpjwG hwdwuuipmiSGbpp K L K pGbpgpwi hwiSwbwpqbpp iSpgb 



A(v P )+4 / .v^L 
A(v P )+f^ 



sA(v f )-(g-±s 2 )^ 



1.10-31 P 



♦ <twjqwbwG dbwipnpjmpjwG hwGwuwpmiSGbpp K b K pGbpgpwi hwiSwbwpqbpp iSpgb 



A(v P )+4^ 



A(vp) + i.v- 



sA( Vf ) - (g - ± s i) 



2 ' C 



1.10-32ui 



51 -82 



4,uijqiulpaiQ -iuipiuphpuiqiuQnipjuiG ^imnniq ShuiupjiuQ 



♦ -iuijlpubuiG dbunpnlumpjuiG hmGmumpniGGbpp K h K pGbpgpmi hwiiwbwpqbpp rfpph 

1 V' 



< 



A(v P )-f^ 
A(v P )-l4 



S A(v P ) + (g-j-S 2 )^ 



1.10-32p 



CQqq&nul 1-26 - (1. 10 - 29)-/7(/ b (l.\0-30)-ni/ inpdwd <iiujbuibiuG huipuipbpwbuiGmpjwG huiwml] inbumpjiuG 
hwbiuqwpd dbiuipnpjmpjwG hwq'wmiipmiSGhpn iShGp Giupnq bGp umwGiui mqpq dbiuipnpjmpjwG hwq'imiwpmiSGhppg 
ipnpjbini[ v P piugmpdwG hwpiupbpwGwG wpwqmpjwG G^wGp: XrduiGwujbu (1.10 - 3lp)-ni/ b (1.10 - 32p)-/7</ inpGwd 
AwjhuiljwG hiupwpbpwGiuGmpjwG hwinmh inbumpjiuG dbiuipnpjmpjwG hiui/iuuuipniii'Ghpn iSbGp Giupnq bGp umwGiui 
hwrfwwiuiniuiipjwGiupiup (1. 10 - 31ui)-/7(/ b (1. 10 - 32m)-ni/ uipduifr dbiuipnpjmpjiuG huidwuwpmiSGhppg GmjGuibu ipnpjbini[ 
v P pwgwpdmb huipwpbpiubuiG wpwqmpjwG G^uiGn: 



Uju puidQp ijkppnuS, npiqhu htuniuppppp oppQuiq, pGGuipqhQp K mqpq pGhpgpuq huiiSuilpjjpqp GlpuuiiSiuiSp a 
hiuuuiuiuiniG uihquiqiuG lupiuquigiSiuiSp 2iupdq'nq, q^npdGuiqiuG duiuQpqp: Ujq q'lnpdGiulpjjQ iSuiuGplip inhqiulpuG 
lupuaqnipjiuQ hiuiiuip dhGp IpiuiuiGuiGp hhuilijuqpuiGuidUp. 

w — a t 

OquiqMqnq' (1. 10 - ll)-ml U (1. 10 - 12)-nL[ uuiMiuGqMiifr puiQiudUhppg U lujGinhq inhqiuqphpiq' inhqiulpuG uipiuqnipjuili 
(1.10- 33)^4 inpqMufr uipiniuhuijimupjiuGp, dhGp hiuuuiuiuiniG inhqiuquiG uqiuiquignuSnq' 2iupdq'nq qhnpdGiuquiG duiuGpqp 
puiguipdiuq uipiuqnipjuiG pq^ujpG U inuipuifruilpuG piuquiqppjGtipp hunSiup IpiuiuiGuiGp hbuiUjuqpiuGuidliipp. 

1 



1.10-33 



? P = y(w~)c = 
v f — yfwjw = 



l+s-^ + g-^- 



1.10-34 



1 +s- 



+ g 



a t 



OquiqMqnq' (1. 10 - 6)-ml uipq\u& piuGuidUpg U (1. 10 - 34)-pg, uinuiGg qM^lluinpuilpuQ Q2iuqpnipjunSp, puigiupduiq 
duiiSuiQuiqp U lipgujquijpp hunSiup iShGp quinuiGuiGp hhinUjuq pujGiudUhpp. 



If^f 



+ g 



a^dt 



1.10-35 



b = ex 



CGq.q&nui 1-27 - UbGp uijibu jbGp giuGbwGniG pjnpwGiui wpwqwgmiSnil 2iupdUnq ipnpdGwlpuG GwuGpGp jimii mji 
qwpiSwGwhpw2 hiuinGmpjniGGhpp Gbp, npnGhbinb qpiuGp GbGp l]2iupiuqpbGp rfhp hiupnpq hnqdwdniG, npp mpi[ GGppdwd 
IpjiGp wqwm GiuiS mdiujpG qiu^mmiS qmGGnq iSwuGpbp GiuiS iSwuGpbGbpp hiuiSiupjrfpp ^lupdiSwG hbmwqnmiSwGp (4uijGiubwG 
huipwphpiubuiGmpjiuG GbpiuGpGiu): Uju ipnpp oppGiuGni/ wwpqiuwbu GbGp giuGbwgwGp dfiwjG G/b[ pb pGjpiuG pGwlpuG 
iSwGiuwiuphnil uuiwgwGp (1.10- 34 )-ni} inpdiud pwGwdbp, npp wpqp hiupiupbpwGiuGmpjwG inbumpjiuG qwuwqppbpm d 
«qmpu t pbpdmd» ludiqiupiupmpjiuGp (wbGpuippmjpG huiGqump pGbpgpui[ hiurfwlpupq h lujiG), npnGhbinh jbG hiupnqwGmrf 
mwppbpwbbi mbqwGwG L pwgwpdwl] wpwqmpjniGGhpn: 



52-82 



Upuj^uiip Injhpp ^uipuiphpiulpjiG CuipdiiuiG ShumpjniQ 



1.11 - ^uijl[uil[uiQ ^uijiuiphpuiljuiQnLpjuiQ ^uiuinilj ShunipjuiQ 
UnuiQdQuihuiuinilj ^l-hiqphpp 

<uijlpjjlpiiG huipuipQpiulpjjQnLpjuiG huiuiniq uihunipjuiG jnpu umuiGdGuihuiuimli qtnqptipp uipdh huiGqimSiuGnptiG 
pGuipqtii; Uhui uijq lunuiGdGuihimnniAj ntnqphpp l}iujuilui& s U g qnpdiuqpg G Dpp hQinLjuiL uipdhpQhppg. 



1) s = 


U 


g = 


2) ,s = 


U 


g*o 


3) s * 


U 


g = 


4) ,s*0 


U 


g*0 



1.11-1 



■EuiGp np inhnuilpjjG U puiguipdiuq lupiuqnipjniQQhpp uiuhiiuiQuijpQ uipdopGopp l}iujuiluj& hG s U g qnp&iulipgQhpp 
uipdhppg, uiupu pQiuquiG t np lihGp (1.11- l)-ni[ inpipiifr pnpip jnpu uinuiGdGuihuiuinli nfciqphpp hiuiSuip s U g 
qnpfriuqpg G Dpp npn2iSuiQ uippnijpQhppQ hunSuiiqujimuuJuiuQ quiGhGp inhnuilpjiG U piuguipduilj uipiuqnipjniQQhpp 
qnjmpjuiG uippmjpQtipp: 



1 . UniuppG LuniuMGiuhujinnilj qhujpp 



s = 
g = 



1.11-2 



♦ Uju qbujppG huimmb lunG^mpjmGGhpp 
Uju uinuiGdGuihuiuiniAi qhiqpfi huniuip, i]hphp2Dl nl l (1.2 - l)-p U (pQijq&nuS 1-10)-p, pQjiqhu QiuU oqinq , hpii[ (1.8 - 8)-ni[ 
inpi[ui& hiuquinjip uipiuqnipjuiG piuGiudLpg U (1.9 - 30)^4 uipu\u& qiuiMui qnpfriuqpg G Dpp puiQiudUhppg, iSUGp IpuiSiujuilpxiG 
w uihnuilpxiG uipiuqnipjujQ hiuiSiup quuiujGuiGp hhuiUjun upujiSiuQQhpp. 

w — w > 

w — —w — —w < 

y(w~) = y(tvj = y{w) = 1 > 



1.11-3 



♦ <Zuijh[ujjpG wGijpmijiupdiliucy dhwipnfiinipjwG himliuuiupmitGhpp 
(1.8 - 15)-ni[ quid (1.8 - 17)-n4 uipu\u& uiuipui&uilpiiG hiujhpaijpQ uiGrunurpupdiiuiG <iujquil}iuQ dUunpnJunipjuiQ 
himliuuiupnuiGtipp iSq$> qppuinhpiil (1.11 - 2)-p U ^oqiniuqnp&hpiq' uMjlpnnpuilpxiG G2UiqpmpjniGp, iShGp IpnniuGuiGp. 



t = t = t 

x — —x = — x 1 



1.11-4 



♦ <Zwpwphpwl]wG 2LupdiSwG dhwipn[unipjiuG hwilwmiipmiSGhpp 
4uii5uiduijG uiju umuiOdGuihuiuiniq qhujpp, (1. 11 - 3)-ni[ U (1.11 — 4)-ni[ inpi[ui& upujiiuiGGtipp qppuinhpii[ (1.8 - 
(1.8 - 26)-ni[, (1.8 - 21)-m[ IpxnS (1.8 - 28)-ni[ inpipiifr ^uijlpulpiiG huipuipbpiulpjjQiupjiuQ huiuiniq uihunipjuiG 
dUuiqhnpampjujQ hiui[iuuuipniiiQtipp iSh$>, pGjiqhu QiuU GmjGiqDu ^oquiuiqnp&tipiil ilhlpnnpuilpjiG Q2iuqpnipjniQp, lihGp 
quuiuiGuiGp Q-uqJuhjp dLiuLpnpjiupjuiG himliuuiupnuiGtipp. 



25) -nil, 



Hinjiq dUunpnlunipjnLQQhp 



4,iulpiiqiupd dUunpnlunipjnLQQtip 



t = t 

x — x' + vt' 



1.11-5 



53-82 



4,uijlpxiquiQ <uipiuphpuil}iuQnipjuiQ ^uiinmAj ShuiupjniQ 



♦ UpiuqmpjniGGbpp hwGiSiuG b qniiSwpiSwG pmGwdhbpp 
f'ul} (1.8 - 29)-ni[ U (1.8 - 30)-ni[ inpqMufr uinuiqnipjniGGhpp hiuQiiuiQ u qnuSuipiiuiG puiGuidLtipp IpnuiipGqGhG luqppajp 
uipuiqmpjniQQtipp hiuQiiuiQ u qnuSuipiiuiG puiGuidLtipp htun pG^iqhu 9 nl J9 t uipqMuft uinnpU. 



u = w — v 
w = u + v 



1.11-6 



♦ SbqmhuiG iupwqmpjmGGbp[i qnjmpjwG m/ipmjpGbpp 



< w < co 



1.11-7 



2. tjpljpnpq mnuiGdUmhuimnili qhujpp. 



s = 
g*0 



1.11-8 



♦ Uju rjbujp[iG hmwml] wnG^nipjniGGhp[i 
Uju umuiGdGuihuiuiiuq qhiqpp huiiiuip, puiGp np s = 0, uiupu (1.8) puidflnui pqMuplpJuifr P n l n P 
uiQhuiiiui^unpnipjmQQhpp i[tpuiQnnS dG: 4,Duiuuipuip pnpip ^ppqplpuqujG i5h&nipjmQQhpp GhGp Ipupnn GGp qpbt uinuiQg 
4hqinnpuiquiQ G2Uiqpmpjuiu'p: OppGuiljp huiiiuip IpuiSuijuilpuG uiDrpulpuG uipuiqiupjiuGGtipp lihGp quipnq hGp oquiuiqnp&tq 
uinuiQg qMilpjinpuilpuG G2Uiqpiupjunip hhuiujuq Ipapiq. 



w — w > 



w — —w 



< 



1.11-9 



X>mjQu}hu puiguipduilj uipuiqmpjuiG pqMujpG U uiuipui&uilpuG puinuiqpp^Qhpp, huniuiduijG (1. 10 - 17)-p lihGp quipnq hGp 
oqinuiqnpdtq uinuiQg qM^quinpuiquiG G2Uiqpiupjuiu'p htunUjuq qhpu}. 



w p = w p ' > 

W, = Wp > 



w p = w p = wj; > 
Wp = — Wp = — Wp < 



Uju hpqpnpq uinuiGdGuihuiinmAj qtuqpp huiiSuip, huniuiduijG (1.9 - 30)-nq\ (1. 10 - 20)-nU_ U (1. 10 - 21)-nU_ uipqMJi& 
puiGuidlibpp, lihGp y qnp&uiljpgQhpp huiiiuip IpnnuiGuiGp hhinUjun uipiniuhuijinnipjnLQQhpp. 



r(w) = r(w) = y(w) = 



l 



i + «- 



= >l l -8-Jt = A(w P )>0 



1.11-10 



1.11-11 



(1.11 - ll)-pg hhinUrmS t np uiDrpulpuG U piugiupduilj uipuiqiupjiuGGtipp upjirip t piuipupiupuG hDuiujuqnpryiiujG 
inppmjpGuppG. 



i + g i V>o 



i-g^r >o 



g*r>-i 



g~t < l 
c 



1.11-12 



♦ 4ujjb[ujj/iG luGijpujijujpdGujfr dbiuifin/unipjiuG hwilwmiipmiSGhpp 
(1.8 - 15)-ni[ quid (1.8 - 17)-nU_ uipipuft uiuipui&uilpuG huijhpujpG wGqpuiquipdipu& dluuipnpmLpjiuG 4uijlpulpuQ 
hiuipuuuipnLiiGtipp iShj qppujntqnq^ (1. 11 - 8)-m[ inpipufr u}uijiiujQp U joquuuqnp(jQpi4 iPalluinpuilpuG G2UiqpnipjniGp, iSuGp 
IpiuiuiGuiQp. 



t = t = t 

x — —x = — x 1 



1.11-13 



54-82 



Upuj^uiip Injhpp ^uipuiphpiuquiG CuipchiuiG ShumpjiuG 



♦ 4wpwpbpwl]wG ^lupdiSwG ^wjhwlpiiG dLwipnlumpjwG hwi[iuuwpmGGbpp 
\>i5uiGuiiqhu (1.8 - 25)-ni[, (1.8 - 26)-nq\ (1.8 - 27)-ni[ U (1.8 - 28)-ni[ inpipufr <iujlpjjlpiiG huipuiphpuilpjjGnLpjuiG 
hiuinmlj inhuiupjuiG 6UunpnJunipjui(i pnpip yipui huiqMjjuuipniiSGhpp lihj Ijppiunhpiq' (1.11- 8)-ni[ uipU_ui& upujiSiuGp U 
GnijGiqhu £oquiuiqnp&hpii[ ilhlpnnpiuquiG G2iuqpmpjiuGp, lihQp quimuQiuQp iJpUQnijQ mqpq U huilpiirpupd dUunpnJunipjuili 
himpiiuuipnuiGtipp. 

Htqpq dUunpnJunipjniQQhp 4,uitpiiquipd 6UunpnJunipjnLQQhp 

*' = 7(v)(« + *-^-*) u \ t = y{v)(t> - g^-x 1 ^ 

x' = y(v)(x- vt) x = y(y)(x' + vt') 



( M ») 2 + g(« P ) 2 = K) 2 + g(w P ) 2 



r>ul[, huiiiuiduijG (1. 10 - 23)-p U (1.11 - ll)-p, uihquilpiiG U piugiupduilj uipuiqiupjmGGhpp lipgU inhqp niQhQ hhuiUjuq 
uinGyupjniGGtipp. 



55-82 



1.11-14 



f'ul} (1.9 - 39)-ni[ inpipiifr iSpjiuquijpp piuGuidUp huiiiiup lihQp IpiuiuiGiuGp hhuiUjuq lupuiuihuijuinipjruGp. 

ti 1 = x{ 2 + gx n = x\ + gx 2 > 1.11-15 

♦ SbqmbmG wpiuqmpjmGGbpp rfppb bqwfr wnG^mpjniGGbpp 

<uu5iuduijG (1.8 - 29)-p, (1.8 - 30)-p U (1.11 - 9)-p, inhrpulpjiG ujpuiqnipjniQQhpp hiuQiiiuQ U qnuSiupiiuiG hunSuip iShGp 
IpjuiuiGuiQp hhuiUjuqpiuQui&Lhpp. 

lIpiuqnipjniQQhpp hiuQiSuiQ piuQiudUp UpuiqnipjniQQhpp qnuiuipiSiuQ piuQiudUp 

u = w ~ y w U w = U + V V1I 1.11-16 

c c 

f»ul} huiu'uiduijll (1.8 - 32)-p U (1.11 - 9)-p, y qnp&iulipgQhpp 6UunpnJunLpjniQQtipp huiiiiup lihQp IpiuiuiQiuQp hhuiUjuq 
puiQuidlihpp. 

r(«) = r(v)r(>f)(i + g-^) 

rM = r(v)rw(i-«^) 

♦ Piugmpdwb wpwqnipjmGGbpJi Gppb bqwir uinG^mpjniGGbpp 
<uu5iuduijQ (1. 10 - 27)-p U (1.11 - 9)-p, puiguipduiq lupiuqnipjniQQhpp iniupiufriulpuG puiquiqppjQtipp hiuQiSuiQ U 

qnuSiupiiuiG hunSuip iShGp IpnniuGuiGp htunLjuiL puiGiudLhpp. 

«p = A(vp)w P - A(wp)v P 
w e = A(v P )wp + A(m p )v p 

t>ul} huiu'uiduijG (1. 10 - 28)-p U (1.11 — 9)-p, A qnp&iuqgp dluuipntuiupjiuG huuiuip lihQp IpiuiuiGiuGp hhuiUjuq 
puiQuidlihpp. 

A(u P ) = A(v P )A(wp ) + g^^- 
c 

A(wp) = A(v P )A( M p)-g^ 



1.11-17 



1.11-18 



1.11-19 



X>i3uiQuiiqhu, huiiiuiduijG (1. 10 - 25)-p, (1. 10 - 26)-p U (1.11 - 9)-p, piugiupduilj uipiuqiupjiuGGapp mqpq U huilpurpupd 
dliUiqhnpampjujQ tuuiSiup iSaGp UuiniuGuiGp hainLjuiL tuuihuuiupnuiGtipp. 

fliqpq dUunpnJunipjniQQtip ^uiquinuipd dUuiqhnpanipjniQQtip 

J K° = "^(Vp'Wp' + gVpWp) J W° = "^(Vp'Mp'-gVpMp) 1.11-20 

Up = -j-(VpV P - WpVp) Wp = -j-(vJm p + MpVp) 

<un5uiduij(i (1. 10 - 24)-p U (1.11 — 9)-p, piuguipduiq lupiuqnipjniQQhpp pipujpQ U iniupiu&iuquiQ puiquiqppjQhpp 
punJuipiupniiS hQ hhinUjun iSQuijniQ uinQ^nipjuiQp. 



1.11-21 



4,uijquiquiQ -iuipuiphpuiquiGnipjuiG ^uiuiniq ShumpjniQ 



1-5- 



1.11-22 



l+g- 



♦ ShrpubiuG h pwgwpdiul] wpiuqmpjniGGhpp qnjmpjmG mppmjpGbpii 
ShnuiquiG h puiguipduiq uipuiqnipjniQQhpp qnjmpjuiQ uiJipnijpQhpp quiQbpii hunSuip iShQp iqhuip t oquiqMjQp 
(1.11 - 9)-pg, (1.11 - 10)-pg U (1.11 - 12)-pg: Ujuujpunil iShQp iqhuip t piidhGp hhuihjuq uiQhuuluiuuipnipjniQQhpp 
huuSuiquipqp. 



w > 



> 



> -1 



1.11-23 



< 1 



(1.11- 23)-ni[ inpipufr uiQhiuqMiiuuipnipjniGGhpp huuSuiquipqp, quipii[iu& g qnp&uiqgp npn2iSuiQ uippmjppg' Q2iuGpg, 
uihnuiquiG h puiguipduiq uipuiqnipjniQQhpp qnjmpjuiQ uiJipnijpQhpp hunSuip iShQp IpiuiuiQuiQp. 



ui) hph g < uuqui < w < c 



p) hph g > uuqui < w < oo 



1 



< If, < CO 



o < w P < C a 



1.11-24 



3. bppnpq uinwGdGwhwuinilj qhiqpp 



s± 
g = 



1.11-25 



♦ Uju ijhujpfiG hmwml] mnG^mpjniGGbpp 
(1.8) puidQnii5 pipupli4uj& pnpip uiQhuuSuijiuipnipjniQQhpp U hhuihuipuip pnpip puiQuidhhpp 1411111141110411115 hQ: UhQp 
uijuuihq qQhpquijuigQhQp lipuijQ uijQ puiQuidhhpp h huuluiuuipniuQhpp, npnGp mQhQ uiliGhuijui muipphpnipjniQQhp: 

■4uu5uiduijQ (1.8 - 9)-p, uiju uinuiQdQuihuiuiniq qtuqpp huiiiuip, (1.9 - 30)-ni[ uipiniifr quiuiSui qnp&uiqpgGhpp IpJiQhQ. 

1 



r(w) 



y(w) 



1^4 



fi+*- 



> 



1.11-26 



fi+s- 



> 



(1.11- 26)-pg hhuiLniiS t np mqpq U huiljuinpp uihnuiquiQ uipuiqnipjniQQhpp puquuqhu punJuipuipniiS hG (1.9 - 32)-ni[ 
inpi[ui& hhuihjuq iquijuuiQpQ. 

1+S&- >0 

1+sf- >0 

(1.11 - 26)-ni[ uipi[ui& quiiMui qnp&uiljpgQhpp puiqMjjpuipniiS hG hhuihjuq uinQyiipjuiQp. 

y(wjy(wj = 1 > 

4uu5uiduijQ (1.2 - l)-p, (1.8 - 8)-p U (1.11 - 27)-p, uihnuiquiQ uipuiqnipjniQQhpp huiiiuip QhQp quuiuiQuiQp hhuihjuq 
uiGhuiq'uiuuipnipjniGGhpp. 



1.11-27 



1.11-28 



56-82 



Upiu^iuip Injhpp <iupiuphpiulpjiQ CiupchiiuG ShumpjniG 



w — w > 

1+sf- >0 

— > 
w = *— 



1.11-29 



1 +.s- 



1 +s- 



< 



f»ul} hun5uiduij(i (1.11- 29)-p, (1.11- 26)-ni[ uipU_iu& qiuiMiu qnpfriu qpg Qhpp uipuiiuhiujuiiliufr mripq uipiuqnipjiuiSp L 
uiniudg qMilpnnpiulpiiQ Q2iuqpnipjuuip, IpJiQhQ. 

1 



/(w) = 



< 



\>i5uiQiuiuhu (1. 10 - 21)-ni[ inpipiifr pjjiirun qnp&iuljgp lupiniuhiujinmpjniGp IpJiQp. 



A(w P ) 



1 + 



1.11-30 



1.11-31 



♦ ^wpwpbpwbwG 2iupdiSwG ^uijbwbwG dbwipnpjmpjwG hunJwuwpmUGbpp 
(1.8 - 15)-ni[ U (1.8 - 17)-ni[ inpipufr hiujhuxijpQ uiQqpuirpupdi[iu& dhiuUintumpjiuQ <iujquil}iuQ huiqMjiuiupniiSQhpp iSQnui 
hQ GmjQp, pulj (1-8 - 25)-nq' uip^uift ^uijlpulpuG hiupiuphpuilpxiQnipjuiQ hiuinmlj inhumpjiuQ mqpq h hiulpurpupfi 
dlouUintunipjiuG hiuiliuuiupniiiGhpp IpiQqniGhG hhinhjuiL uihupp. 

niqpq dliiuipnlunipjniQQhp 4,iulpiiqiupd 6UuupnJunipjnLQQhp 

?' = r (y)~t 

X_,. Li 

]?— ~V t J 

XiiJuiQunqhu (1.8 - 26)-ni[ inpipufr ^lujlpulpuQ hiupiuphpiulpjiQnipjiuQ huiuimq inhumpjiuQ mnjir^ U hiulpuqiupd 
dloudintunipjiuQ hiuiliuuiupnuiQhpp lipQqmQhQ hhinhjuiL inhupp. 




fliqpq dliUupnJunipjniQQhp 

~' = r(v)V 

7 = y(y)\x -*v t\ 



hiulpuqiupd dUiuipnlunipjniGQhp 

V = r(V)T 



t>ul} (1.8 - 27)-ni[ inpipiifr ^uijlpaalpiiG hiupiuphpiulpjjQnipjiuG hiuuinili inhumpjiuQ dhiuipnJunipjiuQ hiuiliuuiupnuiQhpp 
llpQqniQhQ hhuiUjuq uihupp. 



V' = r(v)(? + 4?) 

x" = -y Cyj (~x - ~v t J 



5" = — 7 (V) f j? — v" f ) 



\>i5uiQiuiuhu (1.8 - 28)-ni[ inpipiifr ^lujlpulpiiQ hiupiuphpiulpuGnipjiuQ hiuuinili inhumpjiuQ dUunpnpampjujQ 
hiuiliuuuipniiiQhpp IniGqniQhG hhuiUjuiL uihupp. 



?' = r(V)(T + 4?) 

~x = -y \yj I'x -*v t J 



~x = -y (y\ [ *x - ~v t ) 



<b2Uit uihuQhtnp, (1.11 - 32)-nil, (1.11 -33)-ni[, (1.11 - 34)-nil U (1.11 - 35) -nil mpiliufr pnpip <uijbuiUuiG 
dLiudintunipjiuG hiuiliuuiupniiilitipp, hiuiSiudiujQ (1.9 - 39)-p, piuiluipiupniii hQ lipjiulpujpp hhuiLjuiL uinQyiipjiuGp. 

b 2 — x Q + sx Q x — x + SX()X = x + sx x = Xq + sxox > 



1.11-32 



1.11-33 



1 . 1 1 -34 



1.11-35 



1.11-36 



♦ ShqwlpuG wpmqnipjmGGbpp iSJipb hijwd wnGjmpjmGGbpp 
ShnuilpjjQ uipiuqmpjniQQhpp (1.7 - 29)-n4 U (1.7 - 30)^4 l}iuiS (1.8 - 29)-nil U (1.8 - 30)-nil uipiluicJ qmiSiupiiiuQ h 



57-82 



4,uijh.uiquiQ -iiupuiphpuilpiiQnipjuiQ ^uiinmlj ShumpjmQ 



hiuQiSiuQ puiQuidLhpp l^jJiQUQ. 

fluipij uipuiqnipjniQQhpp huiiiuip 



w — U + V + s - 



u = w + v + s- 



w — V 



^uilpunjip uipuiqnipjniQQhpp huiiSuip 



w = u + v + s- 



u — w + v + s- 



1+*1 



1 + s- 



1.11-37 



(1.11 - 37)-ni[ inpipiiiJ inhnuilpuQ uipuiqnipjniQQhpp qniiiiupiSiuQ U liuiQiiuiQ puiQuidhhpp lipuijQ mnjiq uipuiqnipjniQQhpp 
huiiSuip uiniuQg qMiljuinpuilpiiQ Q2UiqpmpjuiQ, huiiiuiduijQ (1.11 - 29)-p, IpJiQhQ. 



w = u + v + s- 



1.11-38 



r>ul} huiu'uiduijQ (1.8 - 32)-p h (1. 11 - 25)-p y qnpdui qpg Qhpp dhuiUinhinipjniQQhpp huiiSuip iShQp IpiinuiQuiQp hhinlijui^ 
puiQuidhhpp qMiljuinpuilpiiQ Q2Uiqpnipjuiiip. 



r(") = r(v")r(w) 
r 0*0 = r(v)r(») 



r(«) = rOO/O* 7 ) 
r(w) = /(V)/(m) 



1.11-39 



bph (1.11 - 38)-p ilhg lippuinhQp (1.11- 30)-p, uiiqui lihQp IpiinuiQuiQp hhinhjuiLpuiQuidhp ninjuj uipuiqnipjniQQhpp 
huiiSuip, uinuiQg i]hllinnpuilpiiQ Q2iuqpnipjuiQ. 

l+ s ^. = (l+ s ^.)(l+ s M.) 1.11-40 



♦ Piugmpdmb wpiuqnipjniGGhpp iSpph hqiucf wnG^nipjmGGhp[i 
(1. 10 — 27)-ni[ inpipiifr puiguipduili lupiuqnipjniQQhpp inuipuifruilpuQ puiniuqppjQhpp hiuQiSiuQ U qniiiiupiSiuQ IjiiQiuG 
QnijQp, piujg (1. 10 - 28)-n4 uipU_ui& A qnp&iuljpgQhpp dhuiipnhimpjuiQ puiQuidhhpp IpJiQhQ. 

A( Mp ) = A(v P )A(w P )-|, 2 ^ 



A(w P ) = A(v P )A( Mp )+|, 2 ^^ 
c 

t>ul} (1. 10 - 25)-ni[ inpipiifr piugiupdiuq lupiuqnipjniQQhpp inuipphpnipjuiQ pqMujpQ U uiuipui&uilpiiQ puirpuijpli^Qhpp 
dhuiUinhinipjuiQ hiui[iuuiupmiiQhpp IppQhQ. 



_»o i <-()->() 

», = -7rV„W„ 



», = -7rV„W„ 



1 A-0-> -»0<- < > \ 

-jrl V p Wp + WpVp + .SVpWp ) 



1 /->0«- <-<)-> _, <- \ 

jl VpWp +W p Vp +5VpWp] 



"bihuQuiiuhu (1. 10 - 26)-ni[ inpipiifr piugiupdiuq lupiuqnipjniQQhpp qmiSiupp pqMujpQ h uiiupiu&iulpuQ puiqiuijpp^Qhpp 
dhuidinhinipjuiQ hiui[iuuiupmiiQhpp IppQhQ. 



1 -»o->o 



1 <-<)<-() 

-^rVpMp 



1 /-><>-> ->0-» -» -» \ 
= -£-( VpWp + M p Vp + JVpUp ] 



1 A-0<- «-0«- <_ «_ \ 
= -£-( VpHp + M p Vp + JVpUp ] 



Piugiupdiuq lupiuqnipjniQQhpp pipiijpQ h inuipuifruilpuQ puiniuqppjQhpp, hiuiSiudiujQ (1. 10 - 24)-p, piui[iupiupmii hQ 
hhinUjuiL iSQiujmQ uinQyiipjuiQp. 



f-»°V , -»°-> /''-"A 2 , <-"<- f^>°\ 2 , -»°-> f<-°\ 2 , <- 0< - 2 
I w p ] + WpWp = I Wp I + JWpWp = l M p) +sUpU P = [u p J +su p «p = c 



t>Q^iuhu QuiU, hiuiiiudiujQ (1. 10 - 23)-p U (1.11 — 30)-p, uihqiul}iuQ U piugiupdiulj uipuiqnipjniQQhpp lipgh uihijp niQhQ 
hhinUjuiL uinQ^mpjniQQhpp. 

> 



f^¥ 



A(w P )-fv^ 



> 



1.11-41 



1.11-42 



1.11-43 



1 . 1 1 -44 



1.11-45 



58-82 



Upui^uiip Injhpp <uipuiphpuilpiiG CuipdiiuiG ShumpjniG 



♦ ShqwhwG h piugwpdwb mpmqnipjniGGbpp qnjmpjwG mppnijpGbpp 
ShnuilpuQ h puiguipduili uipuiqnipjniGGhpp qnjmpjuiQ uippmjpQhpp npn2hpu huiiiuip QhQp iqhuip t oqim[bQp 
(1.11- 29)-pg U (1.11 — 45)-ni[ inpipiifr puiguipduili uipuiqnipjuiQ puiQuidLpg: Ujuiqpunil iShQp iqhinp t rnidhQp hhuihjuq 
mQhuiqMiiuuipnipjniQQhpp huiiSuiluupqp. 

w > 
l+sf >0 

,., — w 



1.11-46 



f^¥ 



> 



4iu]m[iu& s qnpfruiljgp npn2iiuiQ inppmjppg* Q2iuQpg, inhnuiluuQ h puiguipduili uipuiqnipjniQQhpp niQhQ qnjmpjuiQ 
hhinUjun uippmjpQhpp. 



J ui) 


hph 


s < 


uiiqui 


< w < — L c 


U 


< Wp < CO 


Lp) 


hph 


s > 


uiiqui 


< W < CO 


U 


< Wp < CO 



1.11-47 



4. Urfhllw[iGi]hujllmp qhujp[i 



s* 
8*0 



1.11-48 



IMpnqg lihp hnqi]uifrt2 Qi[ppilui& t hhQg uiju uiiihQuipQnhuiQmp qtuqpp hhuiuiqmnu'uiQp: UjQiqhu np uijuinhn QhQp 
qpQQuipqhQp iJpuijQ inhnuiluuQ h puiguipduili uipuiqnipjniQQhpp npn2iSuiQ mppnipQhpp: 

♦ SbqwbwG wpwqmpjmGGbp[i qnjmpjwG m/ipmjpGbpp 
UJuujuiUi uiuipui&mpjuiQ iShg inhnuiluuQ uipiuqnipjuiQ qnjmpjuiQ inppmjpp npn2hmi hunSuip, uipuiqnipjuiQ mijpq quid 
huiquiqpp lliQhip quiploip jt h hhinLuipuip uiju uiiShQiupQqhuiQmp nhiqph hunSuip QhQp ljuipmj hQp npn2tq inhnuiluuQ 
UipuiqnipjniQQhpp qnjmpjuiQ uippmjpQhpp, l}iujuq'ui& duiiiuiQuilRuuiuipui&mpjuiQ luunmgihij&pp pQmpuiqpnq s u g 
qnp&ui qpg Ghpp npn2iSuiG uippmjpQhppg: Ujuujpuml iShQp ujhuip t midhQp (1.9 - 32)-ml uipihii& uiQhuiiluiuuipmpjniQQhpp 
liuiiSuilpupqp l}unSuijuil}uiG qpuilpuQ w inhnuiluuQ uipuiqnipjuiG huuiuip, pQ^iqUu gmjg t uipihii& uuinpL. 

w > 
l+sf >0 

l+S^r+g^ >0 
C 

(1.11 - 49)-m[ uipihiifr uiQhuiq'uiuuipnipjniGGhpp hunSuiluupqp lihQp Ipupnq hQp qptq GuiU hhuihjuq uihugnq 1 . 

> 



C + 2g 



g-a*r 



> 



(1.11- 50)-Ji lipuijG uinuijpG U hplmnpij uiQhuuhuuuipmpjniQQhppg ppamiS hQ uihnuilpuQ uipuiqnipjniQQhpp hhuihjuq 
qnjnipjuiG uippmjpQhpp, Ipiapiiluifr duiiSuiQuiljuiuiuipuicniipjmQp pQmpuiqpnq s qnp&uiljgp npn2iSuiG uippmjppg* G2iuGpg. 



r i) tpt 


s < 


uiiqui 


< w < — L c 


\ 2) hph 


.v > 


UlUJUl 


< W < CO 



1.11-49 



1.11-50 



1.11-51 



l>ul} (1.11- 50)-p hppnpq uiQhuiq'uiuuipnipjniGp QhQp h_uipnq hGp uipnhh^hphp hGpuiqhuiphpp l}iujuq'ui& g qnp&uiqgp 
npn2iSuiG uippmjppg hhuihjuq l}hpu[. 



59-82 



4,uijl}iuliuiQ -iuipiuphpiulpxiQnipjiuG ^uiinnilj ShumpjmQ 



ui) g >(-§-*) 

p) < g <(|5) 2 

q) g<0 



1.11-52 



Ujchi ilhppufrhQp (1. 11 - 52)-ni[ uipi[iu& hQpiuqhiqphpJig jnipiupiuGympp (1.11- 51)-p hhin hiuiSiuinhij: 

uj) bpp g >(ys) luupii (1.11- 50)-p hppnpq luQhiuihiiuiupnipjiuQ diupj Ipindp fiulpiuqhu iip2in lllhGJi 

ijpiulpuQ dh&nipjniQ U hhuihiupiup w uihniulpxiQ uipiuqnipjniQp Ipupnij t niQhGuiL guiQlpugiud (ijpiulpuQ) 
uipdhp: Uj Qmhhinh hiuiiiuuihnhpnl uijq qnjnipjiuQ infipnijpp (1.11 - 51 )-ni[ inpihufr qnjnipjiuQ uippmjpp hhin, 
ilhQp iuju hQpiunhiqph hiuiSiup IpiuiiuQiuQp uihniulpiiQ lupiuqmpjiuQ hhinUjui^ qnjnipjiuQ uiJipmjpQhpp: 




1.11-53 



p) bpp < g <(y.s) luupii (1. 11 - 50)-p hppnpq luGhiuiliuuiupnipjniQp iShQp Ipupmj hGp qph^hhuilijun 
bhpu}. 



ill + ^L ) > ( I S \ 8 > 



2 § J g 

(1.11 - 54)-ni[ inpihiifr luGhiuqMjiuiupnipjiuG uipiSiuinGhpp IpJiGhG 



W2 = 



|(t*-M s > 2 -*) c 



£uiQJi np ujju hQpuiqhuipJi hiuiiuip g > 0, hhuihiupiup W\ h Wi lupiiiuuiGhpp iSpjU iip2in inhnji mQp hhuihjiUL 
uinGyiipjniGp. 

-ihinhiupiup, huniiudiujG (1.11- 56)-p, iuju hGpiunhiqph huniiup (1.11- 54)-niJ uipihii& luGhiuihiiuiupnipjiuG ilhg w 
inhrpulpuQ lupiuqmpjiuQ hplpu qnjnipjiuQ uiJipnijpQhpp IphQhG. 



w < W\ 



W > W2 



(1.11- 57)-ni[ inpi[m& mGhiuihjiuiupnipjniQQhpp hiuiiiuuihq pii&hpii[ (1.11- 51)-ni[ inpihufr uiGhiuihjiuiupnipjniGGhpp 
hhin, dhGp i^hpgQuiljiuQuiLLihu, iuju hGpiunhiqph hiuiSiup, IpnniuGiuGp inhrpulpuQ lupiuqmpjiuQ hhmhjuq qnjnipjiuQ 
inhpmjpGhpp. 



1) hph < g < (y.s) h s < luupii < w\ < -znrC < W2 hhuihiupiup < w < w\ 

2) hph < g < (y.s) h s > luupu wi < wi < — j- c < hhuihuipuip < w < oo 



1 . 1 1 -54 



1.11-55 



1.11-56 



1.11-57 



1.11-58 



q) bpp g < luupu (1.11 - 50)-fi hppnpij luGhiuqMiiuiupnipjniGp dhGp Ipupnq hGp qph^ hhuihjiUL Iphpiq. 

^h2in t huuinqi[ht, np uiju hGpiunhiqph hiuiSiup, luGlpuhi s qnp&iuljgp Q2UiQpg, (1.11 - 55)-ni[ uipi[ui& W\ uipiiiuuip 
iSp2Ui qpuiljiuQ t pulj Wt uipiiiuuip iip2Ui piugiuuiuljuiQ. 



^2= 4g^is-^^ S ) 2 - g y<o 



1.11-59 



1.11-60 



60-82 



Upuj^uup Injhpp ^uipuipupuilnuG CuipchiuiG ShumpjiuG 



UjupQpQ, huuSuiduijG (1. 11 - 60)-p, w\ u wt uipiiuiuiGapp iSpjU iip2in inhrip mQp hhuiujuiL uinQ^nipjniQp. 

W2 < < W] 

■{hinLuipuip, huiiiiuduiju (1.11- 61)-p, uiju uGpuinhuipp huuiuip (1. 11 - 59)-niJ uipipuft iuQhiui[iuuiupnipjiuQ huiduip w 
inhrpiilnuQ uipuiqiupjiuQ qnjiupjuiQ inppiujpp IpJiQp. 



\W2 < W < Wl 



(1.11 - 62)-ni[ inpipufr uiQhuiipuuuipnipjiulIp hiuiiuiuiaq uu&anii[ (1.11 - 51 )-ni[ inpipufr uiGhujipuuujpiupjnillllapp hhin, 
tShQp i[tip?QiuliuiQuiu}liu, uiju hQpuintiu[pp huuiuip, IpiuiuiGuiQp uihnuilpiiQ uipuiqrupjuiG htnnujuiL qnjnipjuiG uippiujpQhpp. 




g < U .v < 
g < U .v > 



uiupu W2 < < wi < rzJ"C htunuuipuip < w < w\ 
uiupu W2 < < wi hhuilaupuip < w < w\ 



1.11-61 



1.11-62 



1.11-63 



ShnuilpuG uipuiqiupjiuQuupp pnpip hQuipuupip qnjiupjujQ inppiujpGhpp inpi[ui(J hQ uuinpU. 



g\s 

g<0 
g = 



s < 



I 0<w<wi I < w < c 



> 



I < w < w\ 



0<w<<» I < w < co 

< g <(y.S')' I 0<W<Wl I 0<W<OO | < W < CO 

g >(^-.v) 2 I < w < — y c I 0<w<t» I < w < co 



flpinhij Wi U W2 uipuaqnipjniQQhpp inpi[ui& hQ (1. 11 - 55)-ni[. 



1.11-64 



♦ Piugmpdwb wpwqmpjmGGbpp qnjmpjwG inppmjpGbpp 
Oquiq'hpiil (1. 10 - 19)-ni[ uipipu& uinGyupjiuGpg, pQjujtiu QuiU (pGnqdmiS 1-24)-pg, iSUGp IpnnuiGuiGp htunUju^ 
uiGhuuluiuuiprupjiuGGtipp huuSuilpupqp, npp U ujhinp t pii&hQp. 

w P > 

wl 
8—T- < 1 



1.11-65 



<uu5uiduijG (1.11- 65)-p, 4,uijl}uiquiQ huipuiptipujl}ui(inipjujQ huunmlj uiQumpjuiG lihg puiguipduilj uipuiqrupjuiG 
qnjnipjuiG uippiujpp l}uijuilui& t iJpuijG dmdmGwlpjjuiuipui&rupjuiG Inunmgipu&pp pGmpuiqpnn g qnp&uiljgp G2iuGpg. 



f 1) bph 


g<0 


U1UJU1 


< Wp < CO 


| 2) hph 


g>0 


U1UJU1 


< w P < cjf 



1.11-66 



Puiguipduilj uipuiqnipjniGGapp pnpip hQuipuu[np qnjnipjuiG uippnijpQhpp uipipuft uG uuinpU. 



g\s 


I 


.v < 


I .v = 




.v > 


g<0 


I 


< Wp < CO 


I < Wp < CO 




< Wp < CO 


g = 


I 


< Wp < CO 


I qnjnLpjmQ jmQp 




< Wp < CO 


g>0 


I 


< Wp < cjf 


| < wp < cj± 





< Wp < cff 



1.11-67 



CGn.q&mu' 1-28 - Updb wmiiGdGwhwmml] G^bi, np wpwqmpjwG iSbdmpjwG iSwupG wpqp ^ppqplpujmG uippnq pwnup 
(dwuGpbp imjupg wpwq jp Ipupnq 2iupdi[bi pb njj umwpwgbi t iSpwjG m iSpwjG wjG upumtiumnil, np ^p u/wpquju/wGi/niG pb 
n"p wpwqmpjiuG dwupG t pjnupp' mbqwbiuG lupwqmpjwG pb pwgwpdwli mpwqmpjwG: 



61 -82 



4,uijlpxiquiQ -iuipiuphpuilpuQnipjuiQ ^imnniAj ShuiupjiuG 



1.12 - cfuiiJuiQuil[uiuiui]iui&uij]iQ 9Uuii|infunipjniQQh]i]i \jhjiljuijuigniiSii 
llruniuuiljuijJiQ ^uii]uiuuifini.iJGb]i]i Sbupnij 



UhQp quipnq hQp lipiujuiip Injhpp hunSiup uipiniu&iluj& 4,iujlpxilpjiG huipuiphpujljuiGnipjujG himniulj inbumpjuiQ 
dLuiipnpmipjuiG himpiiuuipnuiGtipp QhplpujuigQh^ QiuU uir|jnmuil}iujpQ himpiiuuipnuiGtipp inhupni[: 1-pui hunSiup iSuGp iuhinp 
t oqim[tiQp (1.8 - 15)-ni[ U (1.8 - 17)-ni[ inpipiifr hiujtiuujpG uiGrunurpupdipiifr ^uijlpulpiiG 6UunpnJunipjuiQ 
huupiiuuipnuiGQppg, pQ^ujbu GuiL ppiup GlpuuiiSimSp tuupiuphpuilpiiG 2uipduuiG i5h$> qinGipiq uplpu iniuppup pQupgpuiL 
huuSiulpjipqupp (1.8 - 25)-ni[, (1.8 - 26)-nq\ (1.8 - 27)-ni[ U (1.8 - 28)-ni[ inpipufr <iujlpjilpiiG dUunpnJunLpjuili 
huupiiuuipnuSGQppg, rpnuGg dug upuhupuGhpiil jmUinrpulpxiGnipjiuGp U duiiiuiQuiq - iniupiufrrupjiuG huppuilpajQiupjiuGp: Ujq 
Gupuuiiuljp huiiiuip Guipi qphGp K 1 U K nu]pi\ U hiuquiqpp hplpu pGhpgpuiL huiiiuilpupqhpp dpgU <uijlpjjlpiiG 
dUuiipnpinipjuiQ huupiiuuipnuSGQpp upuhuiQ2ilui& lpupqni[: 

♦ 4wjl]iubwG dbwipnpjmpjwG hiuGwuwpmilGbpp K L K iSpwjG mqpq pGbpgpwi hwiSwbwpqbpp iSpgL 



fluipri dUuiipnpinipjmQQhp 
x=-y(?)3r(c7) +7 (v)x 



<uilpurpupd dUuiipnpinipjmQQhp 

= r(V)(i + 4)(c?') + ,r(V)l 

= -r(V)^(c/) + y(V)?' 



1.12-1 



♦ 4wjl]iubwG dbwipnpjmpjwG hiuGwuiupniilGbpp K b K tlpwjG hwqiuqpp pGbpgpwi hwiSwbwpqbpp ifppb 



flu]pri dUujipnpinipjniQQhp 

cV = r(?)(c7)- g7 (y)3-<x 

-'-r(v)f( c V) + r (^)(i + 4)5 



<uilpurpupd dUujipnpinipjniQQhp 

•V = r(V)(cV') -gy(y)^-x' 

f = y (v)i( c r') +r (v)(i + 4)s 



1.12-2 



♦ 4wjuwbwG dbwipnpjmpjwG hwUwuwpmiSGbpp K hwbwqpp b K mqpq pGbpgpwi hwiSwbwpqbpp rfpph 



V' = y(v)(ct) + y(J)(s + g^-y 

r ' = Kv)f (ct)- 7 (v)t 



c7 = 7 (y)(c7') +7 (y)(s+gj-y 



1.12-3 



— V <— 

♦ 4iujl]iul]iuG dhiuifmfampjiuG hiui/iuuiupmifGbpp K mijpi] h K hmlpurifip ]iGbpg]iiu[ hmGiulpupqhpfi rffipL 

c ?' = y (i9(i + 4)cV + 709[*( 1+ 4)-*l-]* 

^ = -r(v)l(cV)- r (^)(i + 4> 



1 . 1 2-4ui 



r( v)(i + 4) c r , +r (v)[,(i + 4)-,i]5 



1.12-4 P 



UhQp dwtiuiGuilpiiinuipuifrrupjuiG diuiiujQuiqp U iniupiuimipjuiG uiniuQgpuipi[tipp Ipupnq uGp GuplpujuigGtiL iShq 
ujniGuilpuQp lunjnmuiqQQprul U hhinUjuq Q2 ul< lP nl PJ ull Sp- 



62-82 



Upuj^uiip Injhpp ^uipuiphpiulpjiG CuipchiuiG ShumpjniQ 



♦ K h K mijpij pGhpgpwi himSiuhwpqbpmii 



ct 

X 



1.12-5 



♦ K L K hwlpuqpp pGbpgpwi hwiSwlpiipqbpmiS 



ct 

x 



1.12-6 



<uii5uiduijG (1. 12 - l)-ni[ U (1. 12 - 2)-niJ uipijui& mqpq U huilpurpiipd 6UunpnJunipjuiQ hujiluiuuipnuSGQpp, pG^ujhu QuiU 
(1.9 - 31)-ni[ U (1.9 — 33)-ni[ inpipiifr puiGiudUhpp, niripri U hiulpurpupd dUunpnJunLpjuili puinuiliniup uir|jnmuil}Qhpp iShGp 
Ipiipnq hGp qphl hhinUjiu^ G2 ua qP n Lpjuiu'p. 



I = r(v) 



I = r(V) 



v_ 

c 



l + .vl ,1 



1 



= r (V) 



r(v) 





1 


"4 




- 


— > 
V 

c 


i+4 


- 


- 


1 


-4 


- 




V 

c 


i+4 





1.12-7 



ImiIj, huniuiduijG (1.8 - 15)-ni[ U (1.8 - 17)-ni[ inpipufr hiujhpoijpQ uiGqpiurpxipdiluifr 4uijl}iuliuiQ 6UunpnJunipjiu(i 
hun[iuuuipniii(ihpp dhunpntunipjuiG puinuilpuup uinjmuuilpi lihGp Ipjjpnq UGp qph^ htunLjuiL G2 ua qpnLpjuiu'p. 



h = 


1 s 
-1 



1.12-8 



OquiUhpiil (1.8-9)-mlU (1.8 - 24)-n^ uipUui& puiQuidliQppg, pG^uhu QuiU (1.9 - 27)-nil U (1.9 - 29)-ml inpipud nuipn U 
hiulpjjqpp huipuipQpiulpjjQ uipuiqnipjniQQtipp huniiup y qnp&uil[pgQhpp piuniulpuum puiGiudLhppg, hQ2in t huiiinqi[til QuiU np 
(1. 12 - 7)-ni[ inpi[ui& ^uijlpulpiiG mqpq U huilpurpiipd dliUnpnJunipjniQQtipp puiniulpuuli iunjnmuiU.GQpp puiipiipuipmu' hQ 
hhinUjun uinQjmpjnLQQhppQ. 



II =e U 


1 


= 


1 


= l 



1.12-9 



\>i5uiQuivnhu hh2Ui t hunJnqilhl np (1. 12 - 8)-ni[ inpipufr huijhpxijpQ uiQqpiurpupdiSiuQ dUunpnJunipjiuQ puinuiliniup 
uinjniuuilip niQJi humujuiihuiuilinipjniuuQpp. 



er- 1 



Ipuii np Qniju t 



& 



= -1 



1.12-10 



OquiilbpiiJ (1. 12 - 7)-niJ uipi[ui& huipuipQpiulpjjQ 2UipchSuiu puinuilpiiuli iunjnmuil}Qhppg u (1. 12 - 8)-ni[ inpipiid 
huijuiuijpG duuiipnpinipjuiG uinjniuuilipg, iSuup l}uipnii QQp IjujqiSb^hhuilijun uinjnmuilpujpQ uipinuiiipjuiu'iQpp, npnGp 
unijuu}Qu hiuQqpuuiQniii qQ puinuilpiiuti uinjniuuiliGQp. 



h| = y(V) 



h| = r (V) 



1 * + si- 

t- -1 



1 *+«i- 

£- -1 



r (V) 



■K 7 ) 



1 +s- 



1 +5- 



<i+4)-4 

,v(i + 4)-4 
-0+4) 



^ 



1.12-11 



^h 



63-82 



4,uijlpuquiLi ^mpiuphpuilpuilnipjuiG ^luinmli ShuiupjiuQ 



(1. 12 - ll)-ni[ uipipufr h, i; U ^ puimulpuup uiqjnmuilpltipp piuinp uipinuiqpjuqiihpp npn2p^Qhpp IpJiQhQ. 



H 



H 



= -l 



M^uitm QuiU h, £, U ^ pmnmljnmp mixjnmuiliQhpp lipjU qnjnipjniQ mQhQ hhinlijui^ uinQjnipjniQQhpp. 

f = hfh 
|=h|h 



1.12-12 



1.12-13 



Ujchi oquiilhpiil (1. 12 - 5)-nq\ (1. 12 - 6)-ni[ u (1. 12 - 8)-ni[ inpipufr uiqjniuuiqiihppg, iShQp Ipupnq hGp (1.8 - 15)-n4 
inpqiufr hiujhpujhG uiGqpiuquipdqiufr ^uijlpulpuG duiuipnpiiupjiuG huiqiuuuipniu'Gtipp qptq wqjnmuilpujpG hiuihuuiupiiuiG 
inhupni[ htunLjuiL qhpu}. 



K' pdhpgpuiL hiuiSuilpupqnuS 



hf 



K pGhpgpuq huiliuilpupqnui 



hf 



ct 

X 


= 


1 s 
-1 


— >' 

Ct 

—>' 
X 



ct 

X 


= 


1 s 
-1 


ct 

X 



\ji5uiGuiiuhu (1-8 - 17)-ni[ inpipufr huijhpujhG uiGqpiuqiupdqiufr ^uijlpulpuG duuiipnpinipjiuG huiqiuuuipiuu'Gtipp iShGp 
Ipupnq hGp qptq uiqjiuuiuquijpG huiqLUUuipiSiuG uihupnq' hhinujuq l}bpu[. 



K' pGhpgpuiL hiuiSuilpupqnuS 



hf 



K pGhpgpuq huiiiuiqiupqnui 



hf 



— >' 
ct 

— >' 
X 


= 


1 s 
-1 


ct 

X 



— > 
Ct 

— > 

X 


= 


1 s 
-1 


<— 

Ct 

<— 
X 



f*uq uijdli t^ oqimlbpiq' (1.12- 5)-nq\ (1. 12 - 6)-nU 1 U (1. 12 — 7)-n\\ inp4ui& uirunmuiqGhppg, lihGp Ipupnq hGp 
(1. 12 - l)-rR[ inpipufr mqhq h huilpuquipd <iujlpuqiuG dhuuhnhinLpjuiG huiqMnuuipniu'Ghpp qptq uinjnuiuiquijliG hiuihuuiupiiuiG 
inhupni[ hhinhjuiL qhpu}. 



Hiqhq dhuiq^nJunipjniQQhp 



§f 



iuitpuqiupd dhuiqinpinipjniGGhp 



fjf 






y(V) 



— > 
v 

6' 



1 



r (V) 



v 
c 



1 



— »' 

A' 



\>iJuiQuiiuhu (1. 12 - 2)-ni[ inpipufr mqhq h hiuquiquipd <iujbuiqiuG dUuiipnpinipjuiQ huiq'uiuuipriHSQhpp iShGp Ipupnq hGp 
qptq uiqjnuiuiqiujhG hiuihuuiupiiuiG inhupni[ hhinhjuiL l^hpiq. 



1.12-14 



1.12-15 



1.12-16 



Hiqhq dhuiipnpinipjniQQhp 



f;f 



4,uitpuqiupd dhiuihnhinLpjniGGhp 



§f 



= r(v) 



l+S-£ 






C'f 

<— 
.V 



= r(v) 



-si 

1+5^ 



(1. 12 - 16)-ni[ U (1. 12 - 17)-ni[ inpipufr mqhq h hiubuiqiupd dhuiq'inpimpjmGGhpp uiqjmuiuqiujpG huiqMuuuipmu'Ghpp 
hpbm qnqiihpp piuqliuiiqiuinqhm4 duipipg h uiqjmuiuqn4 U hh2tqm[ Giuh (1. 12 - 14)-nU_ U (1. 12 - 15)-n4 inpq\u& huijtqiujhG 
uiQqpuiquipdi[ui& dhuupnpimpjiuG uiqjmuiuqiujpG hiuqMjjuiupnuSGhpp, lihGp buuiuiGuiQp (1. 12 - 3)-nU_ U (1. 12 - 4)-n4 mpq^uift 
dLiUiLhnpinipjniQQhpp uiqjmuiuquijpG huiq^uiuuipiuiSQcipp. 





1.12-17 



1.12-18 



64-82 



Upuj^uiui Injhpp <uipuiphpiuquiG CuipdiiuiG ShumpjniQ 



1.13 - ^bjipuipuiG ljuiiS UiSi|im|iniiJ 



^uijlpulpiiQ <uipuiphpiuquiGnLpjiu(I 4,unnniq ShunipjniGp huipmuui t Qmpp U qdqMup piipGtqp, 2iuin qhiqpDpniiS uinopjui 
l}hQuunpnpdpQ huilpuunq uiGuupuuDip qiuqunpuipQbpni[: ftp uiju hnqi[ui&p iSpuijG jp pGnhuiGpuigGnuS iSpG^U lujdiS Drpu& 
inhuiulpuG uipryrnQpOtipp, uiji uiniuQg npUt uuiMiuQunpuilpiuiG, liuipnip dmptuSiuinpquilpxilI linuihgiSiuQ lipgngnij, ipnpfiniiS t 
pQ^-np tip QnpnipjmQ ni piupiimpjniQ liingQh^ hiupiuphpuil}iuQnipjujQ hiuinnilj inhuiupjuiQ qiunuiqhiupGhpp inmuipiuGiSuiG U 
tJhqGuipuiGu'uiG huipghpnui U mqnhG2nLii t fiuiGiuupuph iSpuigjuiL nui2Uip inhumpjiuQ IpumugiSiuG huiiiuip: 

GQphpgnqp Ipupnq t Qqujintq, np iShp hnrplui&niiS, lipiujuiip ^JiqplpxiquiQ inuipiudnipjuiQ lihg, diuiSiuQuilpi U 
inuipiu&mpjnLQp, puigiupduilj uipuiqmpjiuQ piunuiqpp^Ghpp U pGnhuiGpuiiqhu pnpip puiguipduiq $pqplpxiquiG iSh&nipjniQQhpp 
piluijpQ U iniupuifruilpjiG puinuiqppjGhpp huiGqpuuiGnui bQ hpl}^unp pi]bp, pulj hnui^unp IppqpquilpiiG inuipui&nipjuiG iSh$> 
ilhpnQ2JuiL lih&nipjmQQhpp pi[uijpQ U inuipiudiulpjiG puinuiqppjGhpp U.hujGn]iuujGuiG puinui^uiip pd 1 t'P : 

■<uijquilpiiG ShunipjmQp liiuphiSiuinplpiphG ujjGpiuQ Imm t h Ipuiniupjuq, np uijQ £p Ipupnq iJiQb^ upiuq: <hinLuipuip iShp 
IpirpSpg uimugi[iu& ^uijquilpiiG 6UunpnJunipjiu(i huiqMjauuipnuSGhpp iqhuip t ipnhmippGhQ LnphQgp dUuiipn[unipjuiQ 
hiuQjuuuipnuiQhppQ h uiiipnqj IppqpquiQ iqhuip t qMjpiuQnpnqdJi: flpn^hhinL LnphQgp dUuiUintunLpjiuQ huiQjuuuipnuiQhpp 
hiuQqpuiuQnuS hQ ^uijquilpiiQ huipuiphpiuquiQnipjiuQ huiuimq uihumpjuiQ dUuidinnanipjuiQ hiuQjiiuiupnuiQhpp tip 2Uiin 
iSuiuQuiilnp qhiqpp, hpp 5 = h g = -1: 

Uju piudGmiJ ludipnip 2iupiuruitiQj) iJhp uiniugiu& Ipuplmp lupryniGpGhpp: 



1 . ■iuijUmbuiG hmpiuphpLuUmGnipjuiG huiwmb whumpjiuG dLuiifinpjmpjwG hwGuiuiupmGGhpp: 



♦ 4injb[ujjpG wGi}pwqwpdq'w& <tujjfyiul/ujG dbwipnfumpjwG hmGuiumpnuSGbpp 



K U K pQhpgpuq huniuilpxipqhpp lipgU 



K U K pGhpgpuiL himSiuquipqhpp iSpjU 



Ct = ct + sx 



ct = ct + .sx 

<— — » 

X = —x 



1.13-1 



♦ •CwjlfiulpnG dhwipnpjmpjwG huiGmuuipnuSGbpp K b K mqpq pGbpgpwi hwiSiulpiipqbpp ilpgb 



flu]pri dUuiUin[unipjni(i(ihp 

7'-r(v)[(i + 4)r +g ^] 



r 00 (?-"??) 



4,uil[uiquipd dUunpnJunipjniQQhp 



t = y 
x = y 



W[( 

(•)( 



»1P +Sfi 



'] 



1.13-2 



♦ 4wjl]iuliwG dbwipnpjmpjwG hwdwuuipmiSGbpp K b K hwljiuqpp pGbpgpwi hwUwljiupqbpp ilppb 



< 


fliripri dUuiLpnhanipjniQQhp 

u < 


<uiquiqiupd dUuiq^nJunLpjniQQtip 

'v = r (v)(r'-^') 



1.13-3 



65-82 



4,uijquiquiQ <uipiuphpuil}iuQnipjuiQ ^uiinmq ShunipjniQ 



♦ Q-wiStlw qnp&wbpgGbpii, hwiSwdwjG (1.9 - 30)-/z b (1. 10 - 20)-/;, niGbG hhuiLjwi wpinwhwjumipjniGGhp[i 



r(") = 
7 (V) = 



i+*-*-+*-V 



l+5^-+g- 



= A(v P )-i.s--^>0 



A(v P ) + i.v^E- > 



1.13-4 



■{uijquiquiQ hmpuiphpuiquiGmpjuiQ huiuimq uihumpjuiQ dUuiipnJunipjuiQ huiqMiiuuipnuiQapp, huiiSuiduijQ (1. 10 - 29)-p U 
(1. 10 - 30)-p, iShQp uipuiiuhuijuiagpGp QuiL v P puigiupduiq huipiuphpiulpuQ uipiuqnipjuuSp: 



♦ 4wjbiubwG dhwipnpjmpjwG hiuGwuiupmilGbpp K L K mqpq pGbpgfiwi hiuiSiubwpqbpp iSppb 



Hiqpq dUunpnJunipjniQQhp 


^uiquiquipd dUuiipntunLpjniQQhp 




f 

7 = 


A(vp)+fv^ 


f +g^x 




f 

7 = 


A(Vp)-1^ 


7 +g-^f x' 


< 


x — 


A(v P )-i,i 


X — Vp f 


U < 


X = 


A(vp) + fv% 


I + v P f 




< J 




V J 



1.13-5 



♦ ■iwjUwbwG dbwipnpjmpjwG hwGwuwpmMbpp K b K hwbmqpp pGbpgpw[ hwtfwUwpqhpli iffipb 



Htqpq dliUnpnJunipjniQQhp 


^uiquiqujpd dUujipnpjnipjniQlitip 




c 

t = 


A(vp)-f^ 






<— 
t = 


A(v P ) + |.s'4 L 


<-' Vp <_' 

t + g—fx 


< 


x — 


A(vp)+fv4^ 


X + Vp f 


U < 


x = 


A(v P )-|^ 


X — Vp t 




< J 




L J 



1.13-6 



♦ LiutSqw qnp&wbpgp, hwdwdwjG (1. 10 - 2l)-p, mGp hbinbjwi wpdbpp 



A(v P ) = Jl-te-is 2 )^- 



1.13-7 



♦ <ZwjhiubwG hiupwpbpwhwGmpjwG hwinnib inbumpjwG dbwipnpjmpjwG hwGwuwpmiSGbpp 
uimuGgpuipObpii pwilwpwpniii bG (1.9 - 39) -nd inpGwd iSpgwbwjpp hbmbjmi UGwjmG wpiniuhwjinmpjiuGp 



b 2 — X() + .SX X + gX — X() + SXqX + gX — Xq + SXqX + gx — Xq + SXoX + gx > 



1.13-8 



2. d-LuduiGmbp, hpUmpnipjuiG L quiGqUuifrfi ipnipnpjmpjniGGhpp 

LnphQgp huipiuphpuiquiGmpjuiQ uihunipjniQpg ppinuS t np quipnq hQ inhnp iuGhQuq iSpuijG 2uipdd l nq 6nnp quipSuignuS, 
2iupdilnr[ duiiSuigmjgp duiiSuiGuiqp qiuGqiuqiuu' u 2uin(h]nn iSuipiiGp qiuQqipudp lia&uignuS: Puijg <uijquiquiG 
huipuiphpuiquiGnipjuiG huiinmq uiQuiupjiuGpg hhinUrmS t, np qiupiq^ud dmuuiGuiquiinuipuidnLpjuiG Ipunmgq'iu&pp 
pGmpuiqpnq s U g qnpdui qpg G hpp iSh&nipjmQpg, 2ujpdd 1 nq dnqp quipnq t u quipiSuiGuq u hpquiptq: I^uq 2 UJ P < ^ l l nr l 
duu5uigmjgp uiQquiquiG duiiSuiGuiqp QnijQiqhu quipnq t u quiGquiqtqU uipuiquiGuq: bi q'hpguivqhu, 2uipdipiq uuipiSGp 
qiuQqq'ui&p l}iupnq t u uiiStq U GUjJjqtq: O-piu hiuiSuip iSbQp hpl}iupnipjiuQ «lpiipiSuiQuq», dunSuiQujlip «qiuQquiqtq» quid 
quiQqq'ui&p «uiiStq» uipuiuihuijuinipjniQQhpp dpnJuuiphQ oquiuiqnp&rmS hQp «q L inq 1 inJunipjniQ» uipinuihuijinnLpjinQp: 



66-82 



Upuj^uiip Injhpp <uipuiphpiulpjiG CuipchiuiG ShumpjniQ 



♦ w uipuiqmpjimtp jwpdi/nq / u bpbmpmpjmG mGbgnq &nqp bpGwpnipjmGp mqpq b hwlpuqpp pGhpgfiuii 
himiiulpupqbpniG, hmiSm&mjG (1.3 - 4)-/z, (1.3 - 8)-/z b (1. 10 - 20)-/;, bmGbGw hbmhjmi i/im/infumpjmGGbpp. 



r(w) i c c 2 



h 



y(w) 



w . „ w 



a , ■> 1 W P 

A / \ 1 Wp 



1.13-9 



♦ fliqfiq I* hwlpuqpp fiGhpgfiwi hwGwUwpqbpmd ^wpddnq dnqfi bpbwpmpjwG wilbigmlifi pmGm&hp 









_> 








Wp 










Al = 


= i - 


- / = 


S"*o 

1 w i 














c 



1.13-10 



♦ w wpwqmpjiuiSp 2iupdi[nq diuiSwgnijgli to uibqwbuiG dwGwGiuu[i inbnqmpjmGp mq[iq L hwbmqpp 
liGbpgpwi hmiimbmpqbpmii, huuim&mjG (1.3 - 15)-/;, (1.3- \9)-p, (1.9-31)-p U (1.10-20)-/, bmGbGw 
hbmbjwi ifinifinlunipjmGGbpp. 



t = yS(w)f u = y(w)fo 



f = yS(w)f = y(tv)f„ = 



1+5-^+g- 



i + s^ + gy^. 



A(w P )-fv^ 



A( Wp ) --§-*-=* 



1.13-11 



♦ fliqfaq It hwbwqpp fiGbpg/iwi hwGwbwpqbpmG 'jwpddnq dwGwgmjgp dwdwGwb/i inhnqmpjwG wi[bigmb[i 
pmGwdbp 



At = t - t = s—^-to 



1.13-12 



♦ w uipwqmpjiuiSp 2iupdi[nq mo hwGqum[i qwGqdwdp mqpq b hwbwqfip pGbpgpwi hwiSwbwpqbpmiS, 
hwdwdwjG iSbp hwpnpq hnqi/wdp, bmGbGw hbmbjwi i/im/mfumpjmGGbpp. 



m(wj = yCwjmo 



= m(wj = y(wjrm) — 



m u 



w , „ w 



i + s^+g 



1+sf + g^- 



A(w P )-f^ 



A(w P )-|.v^ 



1.13-13 



♦ fliqfaq li hwbwqpp fiGbpg/iwi hwGwbwpqbpmG ^wpddnq GwuG/ibp qwGqi/wdfi wdb[gmb/i pwGwdbp 



Am = m — m — smn-r = sm J 



1.13-14 



67-82 



4,uijlpuquiQ <uipiuphpuil}iuQnipjuiQ ^imnniAj ShuiupjniQ 



3. SbqwlpuG L pujgmpdwh wpwqnipjmGGhpp qmrfwpifwG L hwGGwG pwGwdLhpp 



♦ Sbqwl]iuG wpwqmpjmGGbpp qmiSwpUwG U hwGiSwG pwGwdbbpp 



1-8- 



l+sjr+g- 



1.13-15 



♦ fiwgwpdwh wpwqnipjmGGhpp mwpw&whwG pwqwqpfcGhpp mwppbpmpjwG U qmiSwpp pwGwdbbpp 



Up = A(vp)wp-A(w P )Vp 
w P = A(vp ) u p + A(wp ) v p 



1.13-16 



♦ fiwgwpdwh wpwqnipjmGGhpp piJwjpG h mwpw&whwG pwqwqpfcGhpp Upgb qnjmpjmG niGbgnq UGwjmG 
wnG^mpjm Gp 



/"-.OV _><)_> /_> n2 A-0N2 <_()<_ ^<_ n2 /->0\2 -><)-> /-> \2 A-<> V <-0<- ^<- \2 

(Wp) +SW p W f +g\W?) = |Wp J +SW p W v +g(W v ) = ( « p I + .S'WpWp + g(_Wp j = I Up] + SUpUp + g{U f J = C" 



1.13-17 



♦ SbqwhwG h pwgwpdwh wpwqnipjmGGhpp iSfiph bqw& wnG^mpjmGGhpp 



= /mv)w = 






r(w) 



A(wp)-i,^£ 



Wp = f(w)w = 



c c 



' v ' A(wp)+ y s c 



1.13-18 



Up JuQqpiuQp lihp hnq^uifrp IpuiS qppnijljp huipquipdiuQ pGphpgnqQhppQ: OuipiuqpiSuiQ lihg uiiquiqpujlpiiQ JjipupuiSGhp 
hiujinGiuphptqm. qhiqpmiS, tuGqpmiS hQp inhqjuiq upuhtq lihq tlblpnpnQuijpQ ipnuinnil: I^uq hph rpup hiujinQiuphphp 
piiuiuinuiuppiulpuQ quiii liuiphiSiuinplpuljuiQ uuijpiupnuSGhp, irnqui Ghpnq IppGhp: 'l-ui iSpiipuijQ lihp lihqpG t U nj ph 
<uijquil}uiQ ShumpjuiG quiii uiniuq'tiL Uu iSiuphiiuiuiplpiijp, nui hhui lihp huiqnpqiuqgnipjniQp uijq upuhpQ Ipxipnq t pnipugtq tp: 



68-82 



Upuj^uiip Injhpp 4uipuiphpiuquiG CuipchiuiG ShumpjniQ 



<uiilhii|ui& 1 - Lpuignig]i^ UuiphiSuiui]iliuiliuiQ PuiQuidUhp 



(1.8) puidQpg v, u U w mqpq U huilpxiqpp uipuiqnipjmQQhpp hiuiiuip lihQp Ipjjpnq hQp uiniuQuiL hhinUjui^ puiQuidUp: 



(l-^)(l-^)(l-^)(l-^)(l-^)(l-^) 



= 1-*- 



l- g - 



1-8- 



M^qhu QuiU hhinlijun hphp puiGuiduhpp. 



(i-sf-)(i- 8 ^) 



■ 8 *$-)(l -,**.) 



1-g- 



f _w -„-s (l-8^-)(l-8^-) 
( l -gVM.)fl- g 3£) = \ cl )\_ el J 

\ C / \ c J I _ uu 

8 c 2 

M-gJiiL )M -J-ffi ) = A c 1 J\ c l J 

V C J V C J 1 „ ww 



V V 

A 



\>i5uiGuiiqhu hhinUjiu^ hphp puiGuidUhpp. 

0-^)(i-^)(i-^)(i-^)^0-. 
0-^)0-^)0-^)0-^) -C 1 -*^) 

UuiiiuijuilpuG w inhquilpuG uipuiqiupjuiG hiuiiuip uihqp niGp hhinLjuiL uinGyupjiuGp. 

1 + ±s$- 

1 + ^.v-^ = 2 —&- 



l + sf 



M^tqhu QuiU hhinUjuq iSGuijiuG uinGyupjniGp. 

^)(i + i'!) = rW(i + i4) = %p) 

\>uili htunujuq uinGyupjniGp. 

/(&)(*£ + y*) + r(™)(gf + t*) = Mr 00 + r(k)] = sA(w v ) 

Shqp niGtiG QuiU htunhjuiL uinQjnipjniQQhpp. 



fliqpq 2iup<JiSuiQ huiiiuip 



4,uiquiqpp 2uipdiiuiQ huiiSuip 



1 +s- 



1 + -S-S-^ 
2 C 



AK)-fv^ 

= A(w f ) 

» , ■> 1 Wp 



6 C + 2 4 -» 

A / N 1 W P 

A(w P )- j-s-±- 



1 + 


«| 


= 


A(w P )-i 

A(w P )+| 


4 

H>P 


1 + 


1* 


w 
c 


A(w 


p) 




— > 








A(wp) + 


i ., w p 

2 C 


w 


+ 


±* 


w c 
8®-F~ 


- J-.sA(w P ) 


A(w P ) 


i w p 

+ —5 — — 
2 C 



4,1-1 
<1-2ui 
41-2 P 
<1-2q 

<1-3iu 
41-3p 
<1-3q 

41-4 

<1-5ui 
<1-5 P 



<1-6 



69-82 



^.uijlpulpoiQ -iuipiuphpuilpuQnipjuiQ ^imnniAj ShuiupjiuG 



^uijlpulpuQ huipuiphpiulpjiGmpjiuQ huiuimli uihumpjiuQ dUimpnpanipjuiQ h\m[iuuuipniii(ihpp lihQp Ipjjpnq hQp qphl GuiL 
IpaiiiuijiulpuG Y(<p,A) $pqplpxilpjjG iSh&nipjiuQ huiiiiup, uipinuihuijini[ui& uihrpulpuG InupuiphpiulpuG uipuiqiupjuiiSp. 



Hiripri dliUnpnJunipjniQQhp 



4,uitpiirpupd fiUunpnJumpjniQQtip 



9=7 



(V)[(l 



l+*+W+8l-A 



A = r(V)(A-l/) 



41-7 



X>i5uiGuimhu ^uijquilpiiG dUuiipnJunipjuiQ huiqMjjuuipniiSGhpp iSUGp l}iupnq hQp qpht IpuiSuijuilpiiG Y(<p,A) $pqplpulpuG 
i5hdnLpjuiG huiiiiup, uipiniuhiujinU_ui& piuguipduilj hiupiuphpuilpxiG uipiuqnipjuiiip. 



fliripq dUuiq^npanipjmQQhp 


^uiquirpupd dloudintuiupjiuGGtip 




9 = 


A(v P ) + i.s'4L 


— > 
<p + g-J-A 




9 = 


A(v,)-i^ 


->' v p 1*' 


< 


A = 


A(v P )-i,% 


"1* v p -» 


A = 


A(v P ) + fs'4L 


A +4^' 




<. 




L - 1 



<1-8 



«<uijlputpiiG <uipuiphpiulpjjQnLpjuiG UhpuiGplpjj» hnrppu&nuS, lihQp ^uijlpulpxiG uihuuiflljjiuGpg niumiiQuiuppiuiS hQp nj 
tipuijG uiquiui liuiuQpljp 2uipdnuip, uijl QuiL hhuiuiqnuinuS hQp iSiuuGpqQhpp hunSiuJuiipp 2iupchSuiG lihpuiGplpiiG: 
PGuitpiiGuipuip uijq qnp&pGpuignuS iShGp oquiuiqnp&nuS hQp puiqnuS Qnp lupimu&ipiifr uinGyupjniGGtipp, npnQp 
llGhplpujuigGtiGp uinnpU uiniuGg uiupugmgiSuiG U IjqphGp lyiiuQp umuiGg UJjlpiinpp G2iuGp: 



«<uijlpulpnG <uipujphpiuqujQnipjiuQ UhpuiQpqui»-niii IpupUnp qhpuil}iuiniupnipjniQ niQhQ hhinUjiUL 
uipiniuhuijinnipjniQQhpp. 



1 + ±sl 



ST + t* 



1 + 2 4 c 



Sf 



1 + -J-J- 



ST 



<1-9 



<hinUjun puiQiudUhpp l}ppuinq'nnS hQ <iujlpjilpuG UhpuiGplpjjjnui tQbpqpuijp upuhupuGiiuiG ophQpp iSh$>. 
(gf + y.v) 2 - .s-fe-^ + fv)(l + y.v-^) + g(l + f^) 2 = te - |-v 2 )(l + *£ + g^r) 

[8(1 + f^)] 2 - ,sfe(l + i*f )]fef + f v) + *fe£ + f v) 2 = g{g - |.s' 2 )(l + *£ + g^) 



<1-10vu 

<1-10 P 



(1 + Y' ? t") U (St - + \ s ) uipuiiuhujjuinipjniQQhpp dUiuq^nJumpjujQ puiQiudUhpp. 

y(«)(i + |*f ) = [r(v)(i + |^)][ r (w)(i + i*J*-)] + (g - | s 2 )rMr(*)^ 
^r(u)(gf + i.v) = [ r (v)fe£ + is)][ 7 (w)(gf + i*>] - fe- |.v 2 ) 7 (v)/(w)(.s'f + s^) 



<1-11 



(1 + yS-Tr-) li fey~ + i" J ) uipuiuihujjuinipjniQQhpp dUiuq^npampjuiQ puiQiudUhpp. 

r(w)0 + ±sf) = [r(v)(i + T 5^)][r(«)(i + T .s-|-)] - eg- x,2 )y(v)y(B) m 
i*r(w)tef- + i*) = [r(v)te£ + l*)][r(«)tef + y*)]-«te- I^M^M") 



<1-12 



70-82 



Upiu^uiqi InjUpfi 4uipuiphpiuquiG CuipdiiuiG ShumpjniQ 



(1 + Y.5-7-) li (g^fr + \s) lupuiuihuijuinipjniQQhpp dUuiipnpanipjmQQhpp iShq luj^piuQuidU. 

f /(«)(i + |. vf ) = r(v){[r(w)(i + |j-f )] + ^[r(w)fef + fs)]} 

1 y(«)tef + i*) = r(v){(i + s })[ 7 (w)fef + |j)] - g^[r(w)(i + !*-*-)]} 



41-13 



(1 + 4-s-TT-) li fe c + 2 5 ) uiptnuihuijinnipjniQQhpp dUuiipntunipjniQQhpp Uhli uiji_puiQuidU. 

f /(w)(1 + J_,_^) = y(v){(l + ji)[y(«)(l + !*£)] - |-[y(«)Q?f- + |j)]> 
1 y(vf)fef- + i*) = y(v){[y(«)tef + fs)] + *£[/(«)(! + y*f)]> 



41-14 



^-Lhpnhp2jun ujpinuihuijinnipjnLQQhpti pjuinQ piuQuidUhp. 






4.1-15 



flpinhq g ffi qnp&iuqpgp niQ{i htunUjuq uipdhpp. 



±,2 

4 ' 



4,1-16 



^uii|h^i|ui& 2 - Q-uiGduiuuip Q-uir\uii|iui]iuiuni[ 3)]iqJil[nuQh]i]i -^uiiSuiji 



LThp huignpq «4wjl]wl]wG <Zwpwphpwl]iuGmpjwG UbpwGpljiu - UJiwjuji/i CwpdmiS» hnrppufriuii uinuigtq hQp piuqntii Qnp 
qiupiiuiGiuhpui2 piuGiudUhp, npnGp GhpqiujuigGnuS hQp ujju huiUJjppjJ&niiS uinuiGg lupuiui&iSuiQ: UpiujQ hp2hgGhQp iShp 
pQphpgnqQhpJiQ, np Ghpqiujuig^nq puiGiudUhpp LnphQgjiuQ huipuiphpiuquiQnLpjuiG uihumpjuiQ hiuiSiupdhpGtipp (hph uijq 
hiuiSiupdhpGhpp phuipqh qnjmpjiuG luGhG) rpup quipnq hp uinuiGuq iShp puiGiudLhppg, qpuiGg lihj s U g qnpfriu qpg Ghpp 
himSiup pGrpuGtqnq' hhuiUjuq lupdhpQhpp. 

'.5 = 

* = -! 



42-1 



1. Shijuil/LuG mpuiqiugniil 

kiuiiuijiulpuQ 2iupdd l nq qnipdGujquiG liuiuQpqJi uihrpuquiG lupiuquignuSGhpp A" L AT' tiGhpgpiiq hiuiSiuquipqtipiuiS iSUGp 
(1.8 - 3)-Ji L (1.8 - 4)-p iShj hiuiSuiupuuiuiupiuiGuipuip uiuhiiuiGtq tpGp hhinUjiu^ qhpiq. 



K mqpq U hujquiqlip pGhpgpuq huiiiuiquipqnui 
Hiqpq uipiuqiugnuS - i 

4uiquiqjip uipuiquignui - c 



K' mqjiq U hiuquiqpp {lQhpgtiuq himSiuquipqmiS 



dw _ d 2 ~x 






dt d~t 2 
dw d 2 x 


<=> 


< 


dt dt 







fliqpri uipuiquignui 
4uiquiqpp uipiuquigrmS 



b = 



d 2 ~x 



du 

dt dt 

du _ d 2 x 



dt 



Oquiuiqnpdhpiq' uihrpuquiG uipiuqiugiiuiQ q'bpnh^juq uuiMuiQnuSp iShGp QhpquijuigGnuS hGp dhq npn2 piuQuidUhp: 



42-2 



71 -82 



4,uijlpuquiQ -iuipiuphpuilpuQnipjuiG ^imnniAj ShuiupjiuQ 



♦ UpLGmjG pGbpgpwi hwiSwhwpqbpmiS ipnpdGwl/wG iSwuGpyp mqpq U hwl/wqpp mbqwpwG 
wpwqwgmiSGbpp iSpph bqwd wnGjmpjmGGbpp (wnuippG pwGwdh) 



K luripri U hiulpuqpp pQhpgpuiL himSuilpupqhpp iSpjU 



K' niripr^ U hiulpuqpp pQhpgpuiL hiuiSiulpjipqhpp iSpjU 



1 



(i + 4) 

i 
(i + 4) 3 



i + j 



c J 



1 + J 



«- V 



<2-3 



♦ UpLGmjG pGhpgpwi hwiSwhwpqbpmiS ipnpdGwqwG GwuGpqp mqpq L hwqwqpp mbqwhwG 
wpiuqwgmiSGhpp iSpph bqwd wnGjmpjmGGbpp (bpqpnpq pwGwdh) 



K nu]pi\ U hiulpuqpp pQhpgpun himSiulpupqhpp iSpjU 



y 3 (wJcT = -y 3 (w~)~a 



K' nii]pr[ U hiulpuqpp pQhpgpuiL hunSiuquipqhpp iSpjL 
7 3 («"")£> = -y 3 (~ujb 



<2-4 



♦ fcpwp GqwwiSwiSp hwpwpbpwqwG 2wpdiSwG iSbp qmGq'nq bpqm mwppbp pGbpgpwi hwiSwqwpqbpmiS 
ipnpdGwqwG GwuGpqp wbqwqwG wpwqwgmiSGbpp GppL bqwd wnGjmpjmGGbpp 



UiuuQpqp nu]pri 2 UJ I 1 <J l i UJ Q huiiluip 



1 



UiuuQpqp huilpuqpp 2iupchSiuQ huiiiuip 



1 



a = 

< 

<— 
b = 


1 


h 


r 3 (v)(i- 


1 A 



r 3 (v)(i + 4 + ^) 



<2-5 



♦ fcpwp GqwwiSwiSp hwpwpbpwqwG 2wpdiSwG itbp qmGq'nq bpqm mwppbp pGbpgpwi hwiSwqwpqbpmiS 
ipnpdGmqwG iSwuGpqp mbqwqwG wpwqwgmiSGbpp iSpph hqwd iSGwjmG wnGjmpjmGGbpp 



Hiripq pGhpgpuiL huiiiuilpupqhpp lipjU 
y 3 (w\a = y 3 (~ujb 



^uilpuqpp pQhpgpun huiiiuilpupqhpp lipjh 



7 3 fw")a" = y 3 Qujb 



<2-6 



UuihiliuQnuI 1-7 - Cwpddnq ipnpdGmqwG iSwuGpqp hwiSwp qnjmpjmG mGbG iSp 2 W PP jmpwhwmml] .ppqpumqwG 
iSbdmpjmGGbp' wpwqwgmiS h md, npnGg pwgwpdwq iShdmpjmGGhpp iSGmiS hG hwuwwmniG primp mqpq hhwqwqpp 
pGbpgpwi hwiSwqwpqbpmiS: "biSwGwwbu qnjmpjmG mGp iSp jmpwhwwmh qwGqi/wd, npn GmjGwbu iSGmiS t hmumwmmG 
pnmp mqpq h hwqwqpp pGbpgpwi hwiSwqwpqbpmiS: Uju prfwpqwd fipqpqwqwG iSbdmpjmGGbpp [wi/wqmjGu bG 
pGnipwqpniiS qwGwjwqwG ipnpdGwqwG iSwuGpqp 2wpdmiSn mdwjpG qw2mmiS: <tbwLmpwp pnmp wjq qwpbnp $>pqpqwqwG 
iSbdmpjmGGbpp iSbGp wGdwGmiS hGp <twjhwl/wG iSbdmpjmGGbp U mwppbpwqmiS bGp qpwGp uwnppG «-4» gmgpjmj: Uhw 
wjq iwjqwhwG .ppqpqwqwG iSbdmpjmGGbpp uwhiSwGmiSp: 



♦ 4wjqwl/wG wpwqwgiSwG uwhiSwGmiSp mqpq L hwhwqpp pGbpgpwi hwiSwqwpqhpp hwiSwp 



a^ = y 3 (wj~a = y 3 (~ujb 
a^ = -y 3 (wJcT = -y 3 (ji^)b 



<2-7 



♦ <twjqwl/wG wpwqwgmiSp pwi/wpwpniiS t hbwLjw[ wwjiSwGGbppG 




42-8 



72-82 



Upiu^uiq"! Injhpp 4iupuiphpiuquiG CuipdiiuiQ ShumpjmG 



♦ 4wjljiubwG qiuGqi/iudp uwhiSwGmiSp 



m t = -(g- jS 2 )mo 



♦ 4wjl]iubwG mdp uuihGiuGniGp mqpq U hiubwqpp pGbpgpwi hwiSwbwpqbpp hwGwp 




42-9 



42-10 



2. Pwgwpdiuli uipiuqwgmii 

kuiiiuijuilpjjQ 2iupdd l nq ipnpdQuiljuiQ liuiuQpljp puiguipfiuil} lupujqiugnuiQhpp K U K' mqfiq U huiquiqpp pQhpgpuq 
hiuiSiuquipqhpmiS (1.10- 9)-p U (1. 10 - 10)-p iSh$> iSbQp muiiuiiqiuinuiutuuiGuipujp uuiMiuGtq tpGp hhuiUjuq Ip^piq. 

K mqpq U huilpuqiip pGhpgpuq muiiuilpiipqnui K 1 mqfiq U huiqujqpp pGhpgpuq huiiSuiqujpqmu' 



fliqpq uipuiquignuS 
4,uilpiiqpp uqiuiquignui 



dw-f 


_ d 2 x> 




dz 


dz 1 


«• < 


dw f 


d 2 X 




dz 


dz 2 





fliq|iq ujpuiquigmii 
4uiquiqpp uipuiqiugnuS 



bo = 



(TUn 



d 2 ~> 



dz 


dz 2 


ctu u 
dz 


d 2 x' 
dz 2 



4,2-1 1 



Oquiuiqnp&hmq' puigiupduiq uipuiquigiSuiG qMjpnhp2Juq uuihiiuiGnuip lihGp GkpquijuigQnui tmp dhq npn2 puiGuidUhp: 
♦ Piugiupdwl] wpwqwgrfwG piuqiuqppjGbpp mqpq pGbpgfiwi hiuiSiubwpqbpmiS (wmiippG pwGm&h) 
K mqpq JiGhpgpuq himSiulpupqiuiS K mqpq fiGhpgpuq huiiSuiqiupqmu' 



< 



->o dw f 4 ,_>n 



(*f + i*)<? 



dwp 
~dz~ 



r«09( 



< 



l + i^la 



->o 


<fi? p 

dz 


fo P = 


du f 
dz 



r 4 (")( 1 + i4)» 



42-12 



♦ fiiugmpduil] wpuiqiugiSuiG puiquiqppjGbpp mqpq pGbpgpui[ hwiiwlpupqbpmii (bpbpnpq pwGmdb) 

— > — »' 

AT mqpq pQhpgpuq himSuiquipqnuS K mqpq pQhpgpuq hunSiuquipqmiS 



'(w~)(g 



r09(i + i4) 



= -y 3 (wn^ = - i 



'00(*£ 



r(T?) i 



2 •* C 



V("w)"fo 



y^Cu^b = a,. 



42-13 



73-82 



4uijlpuquiQ 4uipiuphpuilpxiQnipjujG 4uiinmAj ShuiupjniQ 

♦ fiwgwpdwb wpwqwgifwG pwqwqppjGbpp niqfiq fiGbpgfiwi hwiSwbwpqbpmiS (bpppnpq pwGwdb) 

K U K luripri pGhpgpuiL huiiiuilpupqhpnui 



«, 



° C 2 

->0 



1+1*1 



1 + f5f- 



= -r(v?)«< 

= -y(u)a < 



♦ fiwgwpdwb wpwqwgGwG pwqwqpfijGbpp hwbwqfip fiGbpgfiwi hwiSwbwpqhpmit (wnwpfiG pwGwdb) 
K hiuquiqpp pQhpgpun huiiSuiquipqnuS K huilpuijpp pQhpgpun hiuiiuilpupqmii 



< 






K 4 (w)(, 



g^ + isya 



< 



1 + ^ \a 



- _ dtu-f 



r 4 (")( 1 + i4)» 



♦ fiwgwpdwb wpwqwgGwG pwqwqpfijGbpp hiubiuqfip fiGbpgfiwi hwdwbwpqbpmG (hpbpnpq pwGwdb) 
K hiuquiqpp pGhpgpuiL hiuiSiuquipqnuS K huilpxnjpp pGhpgpuiL huiiiuilpupqnui 

-y 3 (\vYa = -a < -; — i — = -y 3 Cu)b = -a z 



< 



/(*)(*¥ + i*) 



r(-)(i + l4) 



< 



= f 3 nv)t? = a i 



r<V>(V| + l*) 



r(»)(i + i4) 



Y i Qu')b = a < 



♦ fiwgwpdwb wpwqwgGwG pwqwqpfijGbpp hwbwqfip fiGbpgfiwi hwdwfiwpqbpmG (bpppnpq pwGwdb) 

K \jl K hiulpuqpp pGhpgpuiL hiuiSiuquipqtipnuS 

-y(w s )a < 

— i^- 6 = ^=" = -/(« )a< 



«^ + i* l + |.v^ 



42-14 



42-15 



42-16 



42-17 



♦ hwbwqfip pwgwpdwb wpwqwgiSwG pwqwqpfijGbpfi bwwp niqfiq pwgwpdwlj wpwqwgGwG 
pwqwqpfi^Gbpfi hbm 



K pGhpgpuiL luuiiuilpiipqnui 



,_0 _>0 -» 

a„ — a„ + sa t 



CI n — CI n 



K' pGhpgpun huiiiuilpiipqnuJ 



+ sb n 



42-18 



74-82 



Upuj^uiip Injhpp 4uipuiphpiulpjiG CuipchiuiG ShumpjniQ 



♦ 4huiuipppp.p pmGiudb 
K nu]pri U huiquiqpp pGhpgpuJL hiuiSiulpjjpqtipnuS K 1 rnqpri U huilpuiipp pQhpgpun huiiiuilpupqhpnui 



a v = \(w e )a i 
a P = \(w e )a i 



fop = \(u e )a i 
bp = A(u e )a i 



42-19 



♦ Paigiupduib wpwqwgGwG piJiuj/iG pujqiuqppjGbpfi b inwpw&wbwG pujqujqpfijGbp/i bwwp 
K nu]pri U huilpjjqpp pGhpgpuiL hiuiSiulpjipqtipniiS K 1 niripri U hiulpiiiipp pQhpgpun huiiiuilpupqhpnui 



A(vfp) 



« < 



_«»_ (g-in 



1 „2l "T _ 1 



sA(w e ) . 



A(vfp) 



*« = (g-|s 2 )-^ + -^A(«„) 
' p A(« P ) 



p " A(« P ) 



42-20 



♦ Puigiupdwh wpuiqiugduiG pi/wjfiG b wwpwdwhwG piuqiuqppjGbpfi niqjiq dbwGinpjnipjwG 
hwGwuwpniiSGhpp K 1 L K niqfiq U hwbwq[ip JiGbpgJiwi hwiSwbwpqbpp iSJiph 



flinhn pQhpgpuiL huiiiuilpiipqhpp lipjh 



A(V P )+|5^ 



4uilpiinpp pGhpgpuiL huiiiuiquipqhpp iSpjU 



A(v P )+|5^E 



A(v P )-i,^ 



t P c Up 



A(Vp)-|5^ 



ip c «p 



42-21 



♦ Puigiupdwh wpwqwgGwG piJwjpG b wwpiu&wbwG pwqwqpfijGbpp hwhwqwpd dhwipnJumpjwG 
hwGwuwpmiSGbpp K' b K mqpq b hwhwqpp JiGbpgJiwi hwiSwbwpqbpp ujipb 



flinhn pGhpgpuiL huiiiuilpiipqhpp lipjh 



4uil}uiqpp pQhpgpun huiiiuiUuipqhpp iip$>h 



A(v P )-l^ 

A(v P ) + i^ 



S-F- 



'p t c (y p 



A(v P )-l^ 
A(v P )+i^ 



■«-?r 



/p T c ^p 



42-22 



♦ fiwgwpdwq wpwqwgGwG pwqwqpfijGbpp pwiJwpwpmiS bG hbmbjwi wnGjmpjniGGbpfiG 
(aiy + sal~a t + g(a ¥ ) 2 = {g- j-s 2 )y 6 (w)a 2 = (fc p J + sb p b t + g(t v ^ = (g - j-s 2 )y 6 (u)~b = (g - \s 2 )a\ 

(tip) 2 + stffr v +g(a f ) 2 = ( g - i,2) 7 "(t?)S- 2 = p) 2 + sb°X +g(t f y = Of- i^ )r 6^V 2 = Of- |s 2 )a< 



42-23 



75-82 



4,uijlpuquiQ -iuipiuphpuilpuQnipjuiG ^imnniAj ShuiupjiuG 



3. Uqimn GimiGpqp qnpfrnqmpjiuG pGuihqpiuui L LiuqpiuGdpiuG $>mGUgpuiG 



<uijlpulpiiQ huipuiphpiulpuGnLpjuiQ huiuimli uihunipjniQpg iupuiui&ilui& pnpip IpupUnp iShfriupjiuQGhpp luQhG uuinppQ «<» 
gntgp^, npujhuqp iShGp imupphpuilihGp qpiuGp impiiGrpulpjiQ hiuiSiuupuuiuiupmiG iJh&nipjniQQhppg: 



♦ K h K mqpq hGbpgpwi hwiiwbwpqbpmii qnpdnqmpjwG pGwhqpwip h LiuqpmGdpwGp 

K nu]pri pGhpgpuiL huiiiuilpiipqnul K nu]pq pQUpgpun huiiiuilpupqnui 



b^-m n c 2 I U+s^ + g^dt 



&< = -m„c 2 } p+s-^ + gJ^-dt 



:W , „ W 



£^- ma c 2 jl+s^r+g- c2 



X i = - mo c 2 1+S-Jr+g 



u . „ u 



<2-24 



♦ K h K hwl]wi}[ip pGhpgpwi hwdwlpupqbpmd qnpdnqmpjmG pGwhqpwip U LwqpiuGdpiuGp 

K hiuquiqpp pQhpgpun hiuiSiulpjipqnuS K huiljuiiipp pQhpgpun huiiiuilpupqnui 



b^-moc 2 \ Jl+sf+g^dt 



&< =-m c 2 I h+s-^r + g-^dt 



£ i = -m Q c 2 J\+s^-+g 



. w , „ w 



<2-25 



♦ Q-npdnqmpjwG pGmbqpwip GbdmpjmGp pnpip mqpq L hwl]iuqpp pGGpgpiui hwdwl]iupqbpniG 
u/iuJiu/ujGijmG t 



42-26 



♦ UpLGnijG pGbpgpw[ hmGmlpupqbpniG mqpq h hwljwqpp LiuqpiuGdpiuG $>niGl]gpiuGhpp l/iuu/p 
K niripq U huilpuijpp pQhpgpun huiiiuilpupqhpiuii K 1 nu]pq U hiulpuqpp pGhpgpuiL hiuiSiulpjjpqtipniiS 



£ t (w) = 



£ i (w) = 



X 4 (w) 



1 +s- 



£ i(™) 



l + sf 



£ i Cuj = 



£ i (uj = 



£^ (u ) 



1 +s- 



X^Cuj 



1 +s- 



12-21 



76-82 



Upuj^uiip Injhpp 4uipuiphpiulpjiG CuipchiuiG ShumpjniQ 



♦ LwqpwGdfiwG f>mGbgpwGbpji mqfiq b hwbwqwpd 4wjbwbwG dbwGmpjmpjwG pwGwdbbpp K' b K 
mqpq b hwbwqpp pGhpgpwi hwdwbwpqbpp dfapb 



flu]pri dUuiipnpanipjniQQhp 



£ i Cuj = 



£ i (uJ = 



c c i 



l+sf+g 



V w 



x <0*0 



l+s± +i 



l + .vl + g^ 



- £ <(p) 



4,uitpiirpup6 dUuiipnpanipjniQQhp 



£ i (wj = -y-y X^Cuj 



l-g- 



X<(w) = 



1 + S-*r + ; 



l-g- 



-£^(uj 



42-28 



4. Uquiin diuuGpup tGhpqpuijp Lpiuipp ^lujUluuluG pwGuidlihpp 



♦ K mqpq b hwbwqpp pGhpgpwi hwdwbwpqbpmd tGbpqpwjp b pwipp ■fiujUwljiuG pwGwdbbpp 
K niripri pGhpgpuiL himSuilpjjpqnuS K huilpurjpp pQhpgpuj^ huiiSuilpjjpqnuS 



-mac 1 = A(w e )moc' 



Pi = 



^+g- 



g^ + i* 



-moC = A(w P )moc 



!+*-?- + *-£- 



-ra»c 



Pi = 



l+S^r + 



st- 



w 

c 2 



L c l 



-mac 



42-29 



♦ flqfiq b hwumqpp tGbpqpwjp b pwipp -iwjbwbwG wnG^mpjmGGbpp 

«— — > 

E < = E < = E < 

P< =-(Pi+ s T E <) 



42-30 



♦ Slqfiq b hwbwqpp pwipp qnidwpp b wwppbpmpjwG <twjbwbwG wnG^mpjmGGbpp 

P i +p i = -sy(wj M + \s^\m a c = s-^E i 
~P i -P~ i = "2(8 " \s 2 )y(wj^m a c = 2m_.vv P 



42-31 



♦ UG2wpd ifmpdGwbwG dwuG/ibp <ZwjbwbwG GbpppG tGbpqpwjp b <twjbwl/wG GbpppG pwipp pwGwdbbpp 
(w = 0) 



£o = m () c 2 

P<o = P<o = Pi 



-sniQC 



42-32 



♦ Id-wpGiJwd bwdfuwi/wp tGbpqpwjp <twjbwbwG pwGwdbp 



E ^ 2W = ^ 2muc2 " *'*• 



42-33 



77-82 



4,uijlpuquiQ -iuipiuphpuilpuQnipjuiG ^imnniAj ShuiupjniQ 



♦ tGbpqpwjp b pwipp mqpq b hmbwqwpd ^mjbwuwG dbwipnpjmpjiuG hwilwuwpniiSGbpp K b K mqpq 
pGbpgpwi hiuiSwliwpqbpp iSpgb 



Hiqpq dUunpnJunipjniQQhp 



^uilpurpupd dliUnpnJunipjniQQhp 



Z-T )-S J c-P< 



g— = r(v) 



s~r = y(y) 



'0*4) 



s-r J + ^-f^'< 



? < = r(v) 



p<--c-U— 



♦ Cmpddnq ipnpdGwqwG ilwuGpqp ippi[ tGbpqpwjp -iuijlpuljuiG piuGiudL[i 



E, V 



c I ' V S, > — JP'< + s(P<) 2 = U"F" J + S [s~r jp\ + g(V<) = gig - \s 2 ){m cf 

(*¥f +s^y i+g ^ i y = fg^pj + s^y' i+ g(p-' i y=g(g-is*)( m ocf 



♦ LppG tGhpqliwjp 4wjl]iuliwG pwGwdhp 

E\ - S(S ~ is 2 )(m c 2 f = g(g- |. S 2 )£ ( 2 , 



<2-34 



<2-35 



42-36 



5 . <Zuijl/uj[/ui(J m d 

♦ 4uijuwbuiG mdp imiipui&uilpuG pwipuijppjGbpp uwhrfwGmrfp mijpij b hwbuiqpp pGbpgpwi hLudwbuipqbpmd 

— »' — » <— ' «— 

ir U ^f niqpq pQhpgpun huiiiuilpiipqtipnLii £ U K huilpuijpp pQhpgpuiL hiuiSiulpjjpqhpnuS 



/< = 



c/7 



/« = 






♦ AmjhmbuiG mdfi pi/uijfiG piuijiuqpfijfibpp umhiimGmiig mqpq b hwbwqpp pGbpgfimi hmiimbmpqbpmiS 



K U K mqpq pGhpgpuiL huiiiuilpupqhpnLii 



+'o , / E. 

dt 



dt V 



K Xl K hiulpuiipp pQhpgpun himSiulpjipqhpnuS 



_'o , f E. 






<2-37 



<2-38 



78-82 



Upiu^uiq"! Injhpp <uqnuptmuiquiG CuipdiiuiQ ShumpjniQ 



♦ -iuijlpubuib mdp mmpmdmlpud pwqwqpfcGhpp pwGmdbbpp mqpq b hwlpuqpp pdbpgpui[ hwdwbmpqbpmd 
K U K mqpq pQhpgpuq muuuiquipqhpmu K U K huiquiqfip pQhpgpuq huuSuiqumqhpmu' 



ft, = ~(S- 1.5 2 )m„r 3 (l?)fc 
ft, = ~(S- js 2 )m„y 3 (w)a 



ft = ~(g- TS 2 )m y 3 (u)b 
ft = ~(S~ js 2 )m y 3 (w)a 



<2-39 



♦ -iuijlpubuib mdp pdmjpd pmqmqpp^Gbpp piubwdbhpp mqpq U hwbmqpp pdbpgpmi hiudwbwpqhpmd 

— »' — » «— ' <— 

K \x K mqpq pQhpgpuq huiuuiquipqhpmu K U K huiquiqpp pQhpgpuq muuuiquipqhpmu 



ft, = -8(8- \s 2 )m ^f(u)b = *-«-/< 



Jo 



ft = -g(g-is 2 )m fy 3 (u)b = g-*-f < 
7< - -gig- is*)mof r 3 ($)t = gf-J < 



42-40 



♦ 4wjpwbwd hwpiupbpwpwdmpjwG hiuwnip inbumpjwG dbp upuhupuddmd ' t "bjnimnGp dbpwGppiujp 
bpppnpq opbGpp, bpb dbGp hjmmndp qwuwbwG mdp ipnpjwpbG oqinwqnpdbdp <Zwjl]wbiiiG mdp, qwuwpiud 
qwGqdwdp ipnpiiuphb oquiwqnp&bGp ■(wjbwliiuG qujGqdiudp b dbppwiqbu uibqwl]iuG wpwqwgdwd ipnpjwpbG 
dbGp oqmuiqnp&bGp ^wjlpubwG wpwqiugmdp: 



K U K mqpq pQhpgpuq huiuuilpxipqhpmu 



f i = -(g- ±-s 2 )m a i = m i a < 
ft = ~(g- j-s 2 )m a i = m i a i 



K U K huilpuqfip pQhpgpuq huuSuilpjjpqhpmu' 



f < = -{g- ±-s 2 )m a < = m i a i 
ft, = ~(g- |i' 2 )moa < = m i a i 



<2-41 



♦ 4wjljiubwG hwpwpbpwljwGmpjwG hwinnil] inbumpjwG dbp upuhupuGdmd bG Gwb IsjmuinGp dbpwGpbwjp 
wmugpG b bppnpq opbGpGbpp: ^uJjbwpwG mdp dbdmpjmGp pnpip mqpq pGbpgpwi hwdwljiupqbpnid Ijiud 
pmnp hwpmqpp pGbpgpiui hwdwl]wpqbpmd upuhupuGdmd t, pub mqpq b huiljuiqpp pGbpgpui[ hwdwpuipqbpp 
dppb ^uijbuipuiG mdp ipnpumd t dpuijG G/uiGp: 



IjjmuinQp uhpuiQplpiijp uinuigpQ ophQpp 



XijnunnGp uhpuiQplpiijp hppnpq ophQpp 





<2-42 



6. fiuiguipdmlj nid 



♦ Puiguipduip mdp muipui&uipuiG puiquiqppjGbpp uwhdwdmdp mqpq b huibwqpp pGbpgpwi 
hiudiulpupqbpmd 



K U K mqpq pQhpgpuq huiuuilpxipqhpmu 



K U K hiuqiuqpp pQhpgpuq huuSuiljuipqhpmu' 



/.= 



/.= 



d~Pt 
dx 

d~Pt 
dx 





<-' dpt 

J f dx 


< 






<7 ^t 

. J p dx 



<2-43 



79-82 



4,uijlpiiquiQ -iuipiuphpuilpuQnipjuiG ^imnniAj ShuiupjniQ 



♦ fiiugiupdmb mdp pdmjpG pmqmqpp^Gbpp uuihdwGmdp 



<2-44 



♦ UJibGmjG pGhpgpwi hwdwbwpqhpmd wqrpiq b hwl]iuqipiq pwgiupdwb mdp pdwjpG b mwpw&wbiuG 
piuqwqpp^Gbpp dppb mbqp niGGG hbuihjmi wnG^mpjniGGhpp 



K pQhpgpuiL huiiiuiljuipqnui 



f = f 



J x* Ipi'P 



K' pQhpgpun huiiiuilpupqnui 



<_o' ->o' 



J ? g J P j 



<2-45 



♦ fiwgwpdwb mdp pdwjpG piuqiuqppjGbpp pwGwdbhpp K b K' mqpq L hmbmqpp pGbpgpw[ 
hwdwbwpqhpmd ' b bwwp 4wjhwl]wG mdp hbm 



K mripri U huiqujqpp pQhpgpu^ hiuiSiuquipqtipniiS 



/, = SiS- \s" 1 )m -§-a < = g-§-f < 



/, = -g(g-\s 2 )m a ^-a i = g-^fi 



K' mqpq U huilpuijpp pGhpgpuiL huiiiuilpupqhpnLii 



c »< - 6 C J < 



c "4 - 5 c J < 



<2-46 



♦ Pwgwpdwb mdp mwpw&wbwG pwqwqppjGbpp pwGwdbhpp K b K 1 mqpq b hwqwqpp pGbpgpw[ 
hwdwbwpqhpmd ' b bwwp <twjhwl/wG mdp hbm 



K mqpq U huiliuiqpp pQhpgpun huiiiuilpupqhpnui 

/, = -(£- T' s ' 2 ) m o/(w)a < = /(»)/< 



AT' mripri U hiuquiqpp pQhpgpuiL hiuiSiuquipqhpniiS 

-»' -» 

/ P = -fe- \s 1 )nn ) y(u)a < = y(u)f i 

«-' <- 

/ P = -te- ^-i 2 )mor(«)«< = r(")/< 



<2-47 



♦ fiwgwpdwh mdp pdwjpG pwqwqpp^Gbpp wpwwhwjwdw& pwgwpdwh mdp mwpw&wbwG 
pwqwqpp^Gbpnd 



K nu]pri U hiuquiqpp pQhpgpuiL hiuiSiuquipqtipniiS 



f = e W-f = e JZ2-f 

J P & c J p 6 c J A 



J P g c J P g c J i 



K' mqpq U hiulpxiqpp pGhpgpuq humiulpxipqtipnui 



f = e—f = s—^f 



/ p g c J p g c J i 



<2-48 



♦ Lppd pwgwpdwl] mdp pwGwdbp K mqpq b hwljwqpp pGbpgpwi hwdwljwpqbpmd 



/_><)\2 _,0-) /-) \2 / -> ->2 \ .,_, N 2 

/<-0\ 2 <-()<- /,- -,2 / <- <-2 \ ,<_ ,2 



<2-49 



80 -82 



UpAu^iuih Injhpp. <iupuiphpiulp-uG CuipchiuiG ShumpjniG 



♦ Lpjiil pwgwpdmli mdfi pwGmdhp K' niqfiq L hwlpuqpp pGhpgpui[ hwrfwlpupqhpmrf 



->0'\ 2 ->0'->' f- 



7 o y+sfX + g(7' p ) 2 = g [\ + sf +g ^)rf p ) -,ti 



<2-50 



♦ Uqqnq pwgwpdwu mdp pujqujqpfijGbp/i mqpq b hiubwqwpd dbwGmpjmpjwG hwi[iuuiupmGGbpp 

Hiqjiq dhiuihnpjnipjmG K' <=> K ^uiqiuquipd dUuiipnJunipjmQ 



/,= 



A(v P )+|^ 



A(v,) --*-*-? 



f +g—f 

J p 5 c ^ p 



Jp C J P 



/p - 



A(vp)-|^ 



A(v P )+i5^ 



f -K—f 
j P & c j P 



J p c J p 



42-51 



♦ -iwhuiqqnq pmgmpdwb mdp pwqiuqpfyGhpfi niqfiq b hwbiuqwpd dbimpnpjnipjwG hmduiuuipmiiGbpii 



Hiqp.q dhiuihnpjnipjniG 



K' <=> £ 



^uilnuqiupd dUuiipnpjnLpjniQ 



A(V P )+|5^ 



A(vp)-1^ 



/ P +g^ L /p 



_ JUL/- 

J P C J P 



/ P 



A(v P ) --§-,-£■ 



A(Vp)+|5^E 



f -K—f 

J p o c J p 



J p c ■* p 



<2-52 



■<iupqiudiuG pQphpgnq, uijuiqhu lihGp Ipupnq hQp iuQi[hp2 2 UJ P IU G UJ 4kL lipuijuiip uiuipiu&nipjuiG hiuiSiup iShp uipiniufriufr 
prqnpni[fiG Qnp piuGiudLhpp. h hiui[iuuiupnuiGhpp. 2phppp: U"hGp Ipxipnq hQp qptq <iujlpuquiG £ili u G lnul Jl 1 G UTjpiuQpl}iujp 
hiuqMiiuiupnuiQhpp IpuiS iShQp Ipxipnq hQp qptq qiuuiiupli uiiupui&nipjiuG tQhpqhinpq puypJiliufrnipjiuQ 4,uijl}iuqiuQ 
hiui[iuuiupnui(ihpp U qMjpjiuiqhu lihGp quipnq hQp qptq QjiupuilpuQ qui2inp- ^uijlpiiqiuQ hiuihxiuiupnuip, npp U huiQqpuiuQnLii t 
liJiiuuGiulpuG qui2in[i hiuqMjjuiupmu'p: 

luGqpmii hii oquiiuqnp&hp dhp hphiulpjjjmpjniGp, npiqhuqp. iqiuuilphpiugGhp ph p.G^iqlnqY'G IpJiGhG 4npnhp2juq 
hiuq'iuuiupniiiQhpp hniujuuh uiiupiu&nipjiuG hiuiSiup i]hll lnn P lu 'l UJ Q inhupni[: 



khggh' Upnpn.pGhpp ^LujphQpp <iujiuuiniuQp 
kttggh' -iujjiuuuiuiG 



81 -82 



4,uijl}iuliuiQ -iuipiuphpuilpxiGnipjuiQ ^imnniAj ShuiupjniQ 



4,r[nLi5Qhp 



1. Edwards W F, "Special relativity in anisotropic space", Am. J. Phys. 31 482-90, 1963 

2. Jean-Marc Levy-Leblond, "One more derivation of the Lorentz transformation", Universite Paris, 
1975 

3. Jian Qi Shen, "Lorentz, Edwards transformations and the principle of permutation invariance", 
Peoples Republic of China, 2008 

4. Shan Gao, "Relativiti Without Light: aFurther suggestion", University of Sydney 

5. Stephenson and Ki/minster, "Special relativity for Physicists", (London, 1958) 

6. Vittorio Berzi and Vittorio Gorini, "Reciprocity Principle and the Lorentz Transformations", (Journal 
of Mathematical Physics), Volume 10, Number 8, August 1969 



Uhp t^hl[ui]inQuij]iQ ^uiughGhpii 

1. U-nphpui IsuiquipjuiG - robert@armeniantheory.com 

2. -iuiju IrwqwpjwG - haik@armeniantheory.com 



<^uijl[uil[uiQ ShunipjuiQ n lui2UinQuil[uiQ kuijptpB 



http://www. armeniantheory. com 



«Pninp C^iSiupinnipjniQQtipp pQrpufinuip uiQgGnui t hhuiUjun hpbp ipnqbpm]; 
UniujpG ipm^ uipdiuQuiGnui t huiiipQrpnuGnip &uiqpuiGpp, 
trplipnpi]. ipm^ huiGqpujnLii t linpuqpG pGrpipiinipjuiG, 

bppnpij ipm^ uijG pGrpuGipu^ t npujhu pGpGpuinpGpjuiG uil}Ghuijui ipuiuin:» 
Uppmp CnuihGhwmhp, Q-hpdwGuigp piSuwuiuhp, 1788-1860 

■iuipquipduiG pCpttpgnq, n"p iJinimiiJ tap Imp uijdd q.inGi]niiS: 



82-82